diff --git a/.agents/skills/lib.sh b/.agents/skills/lib.sh
index 9dfc327..980ee89 100644
--- a/.agents/skills/lib.sh
+++ b/.agents/skills/lib.sh
@@ -432,7 +432,7 @@ except Exception:
       split_dir=""
       if [ -n "$sample_pane" ]; then
         layout_raw=$(_real_herdr pane layout --pane "$sample_pane" 2>/dev/null || echo "")
-        read -r split_dir split_target < <(printf '%s' "$layout_raw" | python3 -m lib_py.layout --min-cols "${MAM_MIN_PANE_COLS:-15}" --min-rows "${MAM_MIN_PANE_ROWS:-0}" --sample-pane "$sample_pane" 2>/dev/null || echo "right $sample_pane")
+        read -r split_dir split_target < <(printf '%s' "$layout_raw" | python3 -m lib_py.layout --min-cols "${MAM_MIN_PANE_COLS:-15}" --min-rows "${MAM_MIN_PANE_ROWS:-0}" --max-cols "${MAM_MAX_PANE_COLS:-2}" --max-rows "${MAM_MAX_PANE_ROWS:-2}" --sample-pane "$sample_pane" 2>/dev/null || echo "right $sample_pane")
         split_dir="${split_dir:-right}"
         sample_pane="${split_target:-$sample_pane}"
       fi
diff --git a/.agents/skills/lib_py/layout.py b/.agents/skills/lib_py/layout.py
index 6f4697f..439ff67 100644
--- a/.agents/skills/lib_py/layout.py
+++ b/.agents/skills/lib_py/layout.py
@@ -68,108 +68,140 @@ def extract_panes(data: Dict[str, Any]) -> List[PaneInfo]:
     return panes
 
 
+def _pane_id(pane: Any) -> str:
+    if isinstance(pane, PaneInfo):
+        return pane.pane_id
+    return str(pane or "")
+
+
+def _right(reason: str, pane: Any) -> LayoutDecision:
+    return LayoutDecision(target_pane_id=_pane_id(pane), direction="right", reason=reason)
+
+
+def _down(reason: str, pane: Any) -> LayoutDecision:
+    return LayoutDecision(target_pane_id=_pane_id(pane), direction="down", reason=reason)
+
+
+def _overflow(reason: str, pane: Any) -> LayoutDecision:
+    return LayoutDecision(
+        target_pane_id=_pane_id(pane), direction="overflow", is_overflow=True, reason=reason
+    )
+
+
+def _full_height_pane(col: List[PaneInfo], area_h: int, tol: int = 2) -> Optional[PaneInfo]:
+    """Single pane that occupies the full column height. Else None (R-2)."""
+    if len(col) != 1:
+        return None
+    if area_h <= 0:
+        return col[0]
+    return col[0] if abs(col[0].height - area_h) <= tol else None
+
+
+def _group_columns(panes: List[PaneInfo]) -> List[List[PaneInfo]]:
+    columns: List[List[PaneInfo]] = []
+    for p in sorted(panes, key=lambda q: (q.x, q.y)):
+        matched = False
+        for col in columns:
+            if abs(col[0].x - p.x) <= 2:
+                col.append(p)
+                matched = True
+                break
+        if not matched:
+            columns.append([p])
+    for col in columns:
+        col.sort(key=lambda q: q.y)
+    return columns
+
+
+def _area_height(data: Dict[str, Any], panes: List[PaneInfo]) -> int:
+    res = data.get("result") if isinstance(data, dict) else {}
+    if not isinstance(res, dict):
+        res = {}
+    layout = res.get("layout")
+    if isinstance(layout, dict):
+        area = layout.get("area")
+        if isinstance(area, dict) and area.get("height"):
+            try:
+                return int(area["height"])
+            except (TypeError, ValueError):
+                pass
+    if not panes:
+        return 0
+    return max(p.y + p.height for p in panes)
+
+
+def _decide(
+    cols: List[List[PaneInfo]],
+    area_h: int,
+    max_columns: int,
+    max_rows: int,
+    min_cols: int,
+    min_rows: int,
+) -> LayoutDecision:
+    """Shared decision table (GUI observation)."""
+    if not cols:
+        return _right("no_panes_default", "")
+
+    # ① New column only from a full-height pane (R-2).
+    if len(cols) < max_columns:
+        fh = _full_height_pane(cols[-1], area_h)
+        if fh is not None:
+            if fh.width > 0 and fh.width // 2 < min_cols:
+                return _overflow("column_width_overflow", fh)
+            return _right("new_column_right", fh)
+
+    # ② Fill the shortest column (leftmost on ties).
+    shortest = min(cols, key=lambda c: (len(c), c[0].x))
+    if len(shortest) < max_rows:
+        bottom = shortest[-1]
+        if min_rows > 0 and bottom.height > 0 and bottom.height // 2 < min_rows:
+            return _overflow("row_height_overflow", bottom)
+        return _down("fill_column", bottom)
+
+    # ③ Capacity reached.
+    return _overflow("grid_capacity_reached", cols[-1][0])
+
+
+def _decide_headless(
+    panes: List[PaneInfo], max_columns: int, max_rows: int
+) -> LayoutDecision:
+    """Same table as _decide, observed from creation order (0x0 panes)."""
+    n = len(panes)
+    if n >= max_columns * max_rows:
+        return _overflow("grid_capacity_reached", panes[-1])
+    if n < max_columns:
+        return _right("new_column_right", panes[n - 1])
+    return _down("fill_column", panes[n - max_columns])
+
+
 def compute_2xk_layout(
     data: Dict[str, Any],
     min_cols: int = 15,
     min_rows: int = 0,
-    max_columns: Optional[int] = None,
+    max_columns: Optional[int] = 2,
+    max_rows: Optional[int] = 2,
     default_anchor_id: Optional[str] = None
 ) -> LayoutDecision:
+    """Balanced 2xK grid. Herdr-supported splits only: 'right' and 'down'.
+
+    GUI and headless share one decision table. Observation differs:
+    geometry grouping vs creation-order column occupancy.
     """
-    Computes optimal target pane and direction to maintain a balanced 2xK grid.
-    Only uses Herdr-supported split directions: 'right' and 'down'.
-    """
+    if max_columns is None:
+        max_columns = 2
+    if max_rows is None:
+        max_rows = 2
+
     panes = extract_panes(data)
 
     if not panes:
-        # no_panes_default: when herdr returns no panes (empty workspace), default to 'right'
-        target = default_anchor_id or ""
-        return LayoutDecision(target_pane_id=target, direction="right", is_overflow=False, reason="no_panes_default")
+        return _right("no_panes_default", default_anchor_id or "")
 
-    # If only 1 pane in workspace
-    if len(panes) == 1:
-        p = panes[0]
-        # In 2xK grid, 1 pane -> 2 panes: split down to create top and bottom rows
-        # Check height overflow only if min_rows > 0 is explicitly configured
-        if min_rows > 0 and p.height > 0 and p.height // 2 < min_rows:
-            # If height is too small for 2 rows, try splitting right if width allows
-            if p.width > 0 and p.width // 2 >= min_cols:
-                return LayoutDecision(target_pane_id=p.pane_id, direction="right", reason="single_pane_height_constrained")
-            elif p.width > 0 and p.width // 2 < min_cols:
-                return LayoutDecision(target_pane_id=p.pane_id, direction="overflow", is_overflow=True, reason="single_pane_overflow")
-            else:
-                return LayoutDecision(target_pane_id=p.pane_id, direction="right", reason="single_pane_height_constrained_unknown_width")
-        return LayoutDecision(target_pane_id=p.pane_id, direction="down", reason="single_pane_split_down")
+    if all(p.width <= 0 or p.height <= 0 for p in panes):
+        return _decide_headless(panes, max_columns, max_rows)
 
-    # Check for Headless mode: all panes have width <= 0 or height <= 0
-    is_headless = all(p.width <= 0 or p.height <= 0 for p in panes)
-    if is_headless:
-        # Headless panes are all 0x0, so columns cannot be counted from geometry
-        # the way the GUI path does. The alternation below (odd -> down,
-        # even -> right) is what builds the grid, so while that invariant holds
-        # the completed-column count is exactly n // 2. If panes were closed and
-        # the shape drifted, an odd n is absorbed by the `down` branch and the
-        # estimate self-corrects at the next even n.
-        n = len(panes)
-        anchor = default_anchor_id or panes[-1].pane_id
-        if n % 2 == 1:
-            # Filling an existing column never opens a new one, so max_columns is
-            # deliberately NOT checked here -- this mirrors the GUI path, where
-            # `fill_singleton_column` also ignores the cap. max_columns is a
-            # growth guard, not an invariant over the existing layout.
-            return LayoutDecision(target_pane_id=anchor, direction="down", reason="headless_odd_down")
-        current_cols = n // 2
-        if max_columns and current_cols >= max_columns:
-            return LayoutDecision(target_pane_id=anchor, direction="overflow",
-                                  is_overflow=True, reason="max_columns_reached")
-        return LayoutDecision(target_pane_id=anchor, direction="right", reason="headless_even_right")
-
-    # Geometry-aware column grouping
-    # Group panes into columns by X coordinate (fuzz threshold 2 cols)
-    sorted_by_x = sorted(panes, key=lambda p: (p.x, p.y))
-    columns: List[List[PaneInfo]] = []
-    for p in sorted_by_x:
-        matched_col = False
-        for col in columns:
-            if abs(col[0].x - p.x) <= 2:
-                col.append(p)
-                matched_col = True
-                break
-        if not matched_col:
-            columns.append([p])
-
-    # Sort each column's panes by Y coordinate (top to bottom)
-    for col in columns:
-        col.sort(key=lambda p: p.y)
-
-    num_cols = len(columns)
-
-    # 1. Check for any singleton column (column with only 1 pane spanning full height)
-    singleton_col = None
-    for col in columns:
-        if len(col) == 1:
-            singleton_col = col
-            break
-
-    if singleton_col is not None:
-        target_p = singleton_col[0]
-        # Check height only if min_rows > 0
-        if min_rows > 0 and target_p.height > 0 and target_p.height // 2 < min_rows:
-            return LayoutDecision(target_pane_id=target_p.pane_id, direction="overflow", is_overflow=True, reason="singleton_height_overflow")
-        return LayoutDecision(target_pane_id=target_p.pane_id, direction="down", reason="fill_singleton_column")
-
-    # 2. All existing columns have 2 (or more) panes -> we need to start a NEW column to the right
-    if max_columns and num_cols >= max_columns:
-        return LayoutDecision(target_pane_id=columns[-1][0].pane_id, direction="overflow", is_overflow=True, reason="max_columns_reached")
-
-    # Target the top pane of the rightmost column to split right
-    rightmost_top_pane = columns[-1][0]
-
-    # Check width constraint on the rightmost column
-    if rightmost_top_pane.width > 0 and rightmost_top_pane.width // 2 < min_cols:
-        return LayoutDecision(target_pane_id=rightmost_top_pane.pane_id, direction="overflow", is_overflow=True, reason="column_width_overflow")
-
-    return LayoutDecision(target_pane_id=rightmost_top_pane.pane_id, direction="right", reason="new_column_right")
+    cols = _group_columns(panes)
+    return _decide(cols, _area_height(data, panes), max_columns, max_rows, min_cols, min_rows)
 
 
 def _env_int(*names: str, default: Optional[int] = None) -> Optional[int]:
@@ -200,7 +232,8 @@ def main():
     parser = argparse.ArgumentParser(description="Compute 2xK grid TUI layout split direction")
     parser.add_argument("--min-cols", type=int, default=_env_int("MAM_MIN_COLS", "MAM_MIN_PANE_COLS", default=15))
     parser.add_argument("--min-rows", type=int, default=_env_int("MAM_MIN_ROWS", "MAM_MIN_PANE_ROWS", default=0))
-    parser.add_argument("--max-cols", type=int, default=_env_int("MAM_MAX_COLS", "MAM_MAX_PANE_COLS"))
+    parser.add_argument("--max-cols", type=int, default=_env_int("MAM_MAX_COLS", "MAM_MAX_PANE_COLS", default=2))
+    parser.add_argument("--max-rows", type=int, default=_env_int("MAM_MAX_ROWS", "MAM_MAX_PANE_ROWS", default=2))
     parser.add_argument("--sample-pane", type=str, default=None)
     parser.add_argument("--json", action="store_true", help="Output full JSON decision")
 
@@ -219,6 +252,7 @@ def main():
         min_cols=args.min_cols,
         min_rows=args.min_rows,
         max_columns=args.max_cols,
+        max_rows=args.max_rows,
         default_anchor_id=args.sample_pane
     )
 
diff --git a/.mam.env.example b/.mam.env.example
index ed4c823..6e39ca4 100644
--- a/.mam.env.example
+++ b/.mam.env.example
@@ -144,8 +144,13 @@
 # Maximum number of columns a workspace may grow to before the engine reports
 # 'overflow' (which makes lib.sh create a fresh workspace instead of splitting).
 # Applies to both measured (GUI) and headless 0x0 layouts.
-#default: (unset -> no column cap)
-# MAM_MAX_PANE_COLS=3
+#default: 2
+# MAM_MAX_PANE_COLS=2
+
+# Maximum number of rows per column before overflow. Default 2 guarantees an
+# even 2x2 grid; do not raise this until a resize-normalisation pass exists.
+#default: 2
+# MAM_MAX_PANE_ROWS=2
 
 # ==============================================================================
 # deploy / distribution source (for forks/mirrors)
diff --git a/tests/test_b19_headless_reconcile_fixes.py b/tests/test_b19_headless_reconcile_fixes.py
index d79008e..ae7903b 100644
--- a/tests/test_b19_headless_reconcile_fixes.py
+++ b/tests/test_b19_headless_reconcile_fixes.py
@@ -28,11 +28,16 @@ def test_bug2_headless_layout_does_not_overflow():
     assert not d_wide.is_overflow
     assert d_wide.direction == "right"
 
-    # 4. Tall pane (split down)
+    # 4. Tall-but-narrow pane: N=1 is always right; 80//2 < min_cols 60 → overflow
     payload_tall = {"result": {"panes": [{"pane_id": "p1", "rect": {"width": 80, "height": 60}}]}}
     d_tall = compute_2xk_layout(payload_tall, min_cols=60, min_rows=20)
-    assert not d_tall.is_overflow
-    assert d_tall.direction == "down"
+    assert d_tall.is_overflow
+    assert d_tall.direction == "overflow"
+
+    payload_tall_wide = {"result": {"panes": [{"pane_id": "p1", "rect": {"width": 160, "height": 60}}]}}
+    d_tall_wide = compute_2xk_layout(payload_tall_wide, min_cols=60, min_rows=20)
+    assert not d_tall_wide.is_overflow
+    assert d_tall_wide.direction == "right"
 
 
 def test_bug3_reconcile_skills_dir_passed_and_fallback():
diff --git a/tests/test_layout.py b/tests/test_layout.py
index f2818a9..857dc56 100644
--- a/tests/test_layout.py
+++ b/tests/test_layout.py
@@ -17,7 +17,7 @@ def test_empty_or_malformed_json_fallback():
     assert not d.is_overflow
 
 
-def test_1_pane_split_down():
+def test_1_pane_split_right():
     payload = {
         "result": {
             "panes": [
@@ -27,8 +27,9 @@ def test_1_pane_split_down():
     }
     d = compute_2xk_layout(payload, min_cols=60, min_rows=20)
     assert d.target_pane_id == "p1"
-    assert d.direction == "down"
+    assert d.direction == "right"
     assert not d.is_overflow
+    assert d.reason == "new_column_right"
 
 
 def test_1_pane_height_constrained_splits_right():
@@ -59,19 +60,20 @@ def test_1_pane_overflow():
     assert d.is_overflow
 
 
-def test_2_panes_to_3_panes_new_column_right():
+def test_2_panes_fill_left_column_down():
     payload = {
         "result": {
             "panes": [
-                {"pane_id": "p1", "rect": {"x": 0, "y": 0, "width": 160, "height": 40}},
-                {"pane_id": "p2", "rect": {"x": 0, "y": 40, "width": 160, "height": 40}}
+                {"pane_id": "p1", "rect": {"x": 0, "y": 0, "width": 80, "height": 80}},
+                {"pane_id": "p2", "rect": {"x": 80, "y": 0, "width": 80, "height": 80}}
             ]
         }
     }
     d = compute_2xk_layout(payload, min_cols=60, min_rows=20)
     assert d.target_pane_id == "p1"
-    assert d.direction == "right"
+    assert d.direction == "down"
     assert not d.is_overflow
+    assert d.reason == "fill_column"
 
 
 def test_3_panes_to_4_panes_fill_singleton():
@@ -88,9 +90,10 @@ def test_3_panes_to_4_panes_fill_singleton():
     assert d.target_pane_id == "p3"
     assert d.direction == "down"
     assert not d.is_overflow
+    assert d.reason == "fill_column"
 
 
-def test_4_panes_to_5_panes_new_column():
+def test_4_panes_to_5_panes_overflows_at_capacity():
     payload = {
         "result": {
             "panes": [
@@ -102,9 +105,9 @@ def test_4_panes_to_5_panes_new_column():
         }
     }
     d = compute_2xk_layout(payload, min_cols=60, min_rows=20)
-    assert d.target_pane_id == "p3"
-    assert d.direction == "right"
-    assert not d.is_overflow
+    assert d.direction == "overflow"
+    assert d.is_overflow
+    assert d.reason == "grid_capacity_reached"
 
 
 def test_4_panes_overflow_when_width_constrained():
@@ -140,33 +143,35 @@ def test_max_columns_limit():
 
 
 def test_headless_0x0_transitions():
-    # N=1 -> down
     p1 = {"result": {"panes": [{"pane_id": "p1", "rect": {"x": 0, "y": 0, "width": 0, "height": 0}}]}}
-    assert compute_2xk_layout(p1).direction == "down"
+    assert compute_2xk_layout(p1).direction == "right"
 
-    # N=2 -> right
     p2 = {"result": {"panes": [
         {"pane_id": "p1", "rect": {"x": 0, "y": 0, "width": 0, "height": 0}},
         {"pane_id": "p2", "rect": {"x": 0, "y": 0, "width": 0, "height": 0}}
     ]}}
-    assert compute_2xk_layout(p2).direction == "right"
+    d2 = compute_2xk_layout(p2)
+    assert d2.direction == "down"
+    assert d2.target_pane_id == "p1"
 
-    # N=3 -> down
     p3 = {"result": {"panes": [
         {"pane_id": "p1", "rect": {"x": 0, "y": 0, "width": 0, "height": 0}},
         {"pane_id": "p2", "rect": {"x": 0, "y": 0, "width": 0, "height": 0}},
         {"pane_id": "p3", "rect": {"x": 0, "y": 0, "width": 0, "height": 0}}
     ]}}
-    assert compute_2xk_layout(p3).direction == "down"
+    d3 = compute_2xk_layout(p3)
+    assert d3.direction == "down"
+    assert d3.target_pane_id == "p2"
 
-    # N=4 -> right
     p4 = {"result": {"panes": [
         {"pane_id": "p1", "rect": {"x": 0, "y": 0, "width": 0, "height": 0}},
         {"pane_id": "p2", "rect": {"x": 0, "y": 0, "width": 0, "height": 0}},
         {"pane_id": "p3", "rect": {"x": 0, "y": 0, "width": 0, "height": 0}},
         {"pane_id": "p4", "rect": {"x": 0, "y": 0, "width": 0, "height": 0}}
     ]}}
-    assert compute_2xk_layout(p4).direction == "right"
+    d4 = compute_2xk_layout(p4)
+    assert d4.direction == "overflow"
+    assert d4.is_overflow
 
 
 def test_real_herdr_080_nested_layout_format():
@@ -211,7 +216,7 @@ def test_cli_invocation_pipe():
         env=env
     )
     assert res.returncode == 0
-    assert res.stdout.strip() == "down p1"
+    assert res.stdout.strip() == "right p1"
 
     res_json = subprocess.run(
         [sys.executable, "-m", "lib_py.layout", "--json"],
@@ -223,7 +228,7 @@ def test_cli_invocation_pipe():
     assert res_json.returncode == 0
     data = json.loads(res_json.stdout)
     assert data["target_pane_id"] == "p1"
-    assert data["direction"] == "down"
+    assert data["direction"] == "right"
     assert not data["is_overflow"]
 
 
@@ -284,10 +289,10 @@ _real_herdr() {{
 sample_pane="p1"
 split_dir=""
 
-# Exact snippet from lib.sh:429-435
+# Exact snippet from lib.sh layout invocation
 if [ -n "$sample_pane" ]; then
   layout_raw=$(_real_herdr pane layout --pane "$sample_pane" 2>/dev/null || echo "")
-  read -r split_dir split_target < <(printf '%s' "$layout_raw" | python3 -m lib_py.layout --min-cols "${{MAM_MIN_PANE_COLS:-15}}" --min-rows "${{MAM_MIN_PANE_ROWS:-0}}" --sample-pane "$sample_pane" 2>/dev/null || echo "right $sample_pane")
+  read -r split_dir split_target < <(printf '%s' "$layout_raw" | python3 -m lib_py.layout --min-cols "${{MAM_MIN_PANE_COLS:-15}}" --min-rows "${{MAM_MIN_PANE_ROWS:-0}}" --max-cols "${{MAM_MAX_PANE_COLS:-2}}" --max-rows "${{MAM_MAX_PANE_ROWS:-2}}" --sample-pane "$sample_pane" 2>/dev/null || echo "right $sample_pane")
   split_dir="${{split_dir:-right}}"
   sample_pane="${{split_target:-$sample_pane}}"
 fi
@@ -297,7 +302,7 @@ echo "SAMPLE_PANE=$sample_pane"
 """
     res = subprocess.run(["bash", "-c", script], capture_output=True, text=True)
     assert res.returncode == 0, f"Script failed with code {res.returncode}. Stderr: {res.stderr}"
-    assert "SPLIT_DIR=down" in res.stdout
+    assert "SPLIT_DIR=right" in res.stdout
     assert "SAMPLE_PANE=p1" in res.stdout
 
 
@@ -360,12 +365,11 @@ def test_cli_max_cols_flag_triggers_overflow():
     assert res.returncode == 0, res.stderr
     d = json.loads(res.stdout)
     assert d["direction"] == "overflow" and d["is_overflow"]
-    assert d["reason"] == "max_columns_reached"
+    assert d["reason"] == "grid_capacity_reached"
 
 
 def test_env_max_cols_applies_without_flag():
-    """MAM_MAX_PANE_COLS is honoured with no --max-cols flag, which is exactly
-    how lib.sh invokes the module (lib.sh passes no --max-cols)."""
+    """MAM_MAX_PANE_COLS is honoured with no --max-cols flag."""
     payload = json.dumps(_four_panes_two_columns())
     skills_dir = os.path.abspath(".agents/skills")
     env = {**os.environ, "PYTHONPATH": skills_dir, "MAM_MAX_PANE_COLS": "2"}
@@ -374,48 +378,37 @@ def test_env_max_cols_applies_without_flag():
          "--min-cols", "30", "--min-rows", "20", "--json"],
         input=payload, capture_output=True, text=True, env=env)
     assert res.returncode == 0, res.stderr
-    assert json.loads(res.stdout)["reason"] == "max_columns_reached"
+    assert json.loads(res.stdout)["reason"] == "grid_capacity_reached"
+
+
+def _headless(n):
+    return {"result": {"panes": [
+        {"pane_id": f"p{i}", "rect": {"x": 0, "y": 0, "width": 0, "height": 0}}
+        for i in range(1, n + 1)]}}
 
 
 def test_headless_max_columns_growth_guard():
-    """C-1: headless mode must honour max_columns too.
-
-    A headless 2xK grid completes n // 2 columns, so at n=4 with max_columns=2
-    a further `right` split would open a third column and must overflow instead.
-    Note the cap blocks *opening* a new column; it does not force an existing
-    over-cap layout to shrink -- the odd-n `down` branch (and the GUI's
-    fill_singleton_column) deliberately ignore it.
-    """
-    def headless(n):
-        return {"result": {"panes": [
-            {"pane_id": f"p{i}", "rect": {"x": 0, "y": 0, "width": 0, "height": 0}}
-            for i in range(1, n + 1)]}}
-
-    d4 = compute_2xk_layout(headless(4), max_columns=2)
+    """Headless capacity: n=1 right, n=2/3 down, n>=4 overflow at max_columns=2, max_rows=2."""
+    d4 = compute_2xk_layout(_headless(4), max_columns=2, max_rows=2)
     assert d4.is_overflow and d4.direction == "overflow"
-    assert d4.reason == "max_columns_reached"
+    assert d4.reason == "grid_capacity_reached"
 
-    # Continues growing below the cap
-    d2 = compute_2xk_layout(headless(2), max_columns=2)
-    assert d2.direction == "right" and not d2.is_overflow
+    d2 = compute_2xk_layout(_headless(2), max_columns=2, max_rows=2)
+    assert d2.direction == "down" and d2.target_pane_id == "p1" and not d2.is_overflow
 
-    # Filling an existing column is not blocked (mirrors GUI fill_singleton_column)
-    d3 = compute_2xk_layout(headless(3), max_columns=2)
-    assert d3.direction == "down" and not d3.is_overflow
+    d3 = compute_2xk_layout(_headless(3), max_columns=2, max_rows=2)
+    assert d3.direction == "down" and d3.target_pane_id == "p2" and not d3.is_overflow
 
-    # n=5 is the first odd n that can discriminate: n//2 == 2 == max_columns, so an
-    # over-correction that also checked the cap on the odd branch would return
-    # overflow here. n=3 has n//2 == 1 and cannot reach the check at all.
-    d5 = compute_2xk_layout(headless(5), max_columns=2)
-    assert d5.direction == "down" and not d5.is_overflow
-    assert d5.reason == "headless_odd_down"
+    d5 = compute_2xk_layout(_headless(5), max_columns=2, max_rows=2)
+    assert d5.is_overflow and d5.reason == "grid_capacity_reached"
 
-    # When max_columns is not set, existing alternation is preserved (behavior neutrality)
-    assert compute_2xk_layout(headless(4)).direction == "right"
+    # Default cap is 2 even when the caller omits max_columns.
+    assert compute_2xk_layout(_headless(4)).direction == "overflow"
 
 
 _LAYOUT_ENV_VARS = ("MAM_MIN_COLS", "MAM_MIN_PANE_COLS", "MAM_MIN_ROWS",
-                    "MAM_MIN_PANE_ROWS", "MAM_MAX_COLS", "MAM_MAX_PANE_COLS")
+                    "MAM_MIN_PANE_ROWS", "MAM_MAX_COLS", "MAM_MAX_PANE_COLS",
+                    "MAM_MAX_ROWS", "MAM_MAX_PANE_ROWS")
 
 
 def _run_layout(payload, args=(), env_extra=None):
@@ -437,14 +430,14 @@ _ZERO_TRAP = {"result": {"panes": [
 def test_j1_env_zero_min_cols_matches_flag_zero():
     """J-1: MAM_MIN_PANE_COLS=0 must mean 0, not fall through to the 15 default."""
     flag = _run_layout(_ZERO_TRAP, ("--min-cols", "0", "--min-rows", "20"))
-    assert flag["direction"] == "right" and flag["reason"] == "single_pane_height_constrained"
+    assert flag["direction"] == "right" and flag["reason"] == "new_column_right"
     for var in ("MAM_MIN_COLS", "MAM_MIN_PANE_COLS"):
         assert _run_layout(_ZERO_TRAP, ("--min-rows", "20"), {var: "0"}) == flag, var
 
 
 def test_j1_env_zero_min_rows_matches_flag_zero():
     flag = _run_layout(_ZERO_TRAP, ("--min-rows", "0"))
-    assert flag["direction"] == "down" and flag["reason"] == "single_pane_split_down"
+    assert flag["direction"] == "right" and flag["reason"] == "new_column_right"
     for var in ("MAM_MIN_ROWS", "MAM_MIN_PANE_ROWS"):
         assert _run_layout(_ZERO_TRAP, (), {var: "0"}) == flag, var
 
@@ -480,26 +473,17 @@ def test_j1b_invalid_alias_does_not_shadow_the_documented_var():
 
 
 def test_default_min_cols_is_15_and_min_rows_is_0():
-    """Verify compute_2xk_layout default min_cols is 15 and min_rows is 0.
-    With 1 pane of 54x23:
-    - min_rows=0 -> splits down without height overflow
-    With 2 panes of 30x23 (width//2 = 15):
-    - min_cols=15 -> 15 >= 15 -> split right (new column).
-    - min_cols=40 -> 15 < 40 -> overflow.
-    Default invocation (no min_cols/min_rows passed) must split right for 30 cols.
-    """
-    # 1. 1 pane of 54x23 splits down (no height constraint)
+    """Default min_cols=15, min_rows=0. N=1 opens a column with right."""
     p1_54x23 = {"result": {"panes": [{"pane_id": "p1", "rect": {"x": 26, "y": 1, "width": 54, "height": 23}}]}}
     d1 = compute_2xk_layout(p1_54x23)
-    assert d1.direction == "down"
+    assert d1.direction == "right"
     assert not d1.is_overflow
+    assert d1.reason == "new_column_right"
 
-    # 2. 2 panes with width 30 (30 // 2 = 15 == min_cols 15) -> splits right cleanly
     payload = {
         "result": {
             "panes": [
-                {"pane_id": "p1", "rect": {"x": 0, "y": 0, "width": 30, "height": 20}},
-                {"pane_id": "p2", "rect": {"x": 0, "y": 20, "width": 30, "height": 20}},
+                {"pane_id": "p1", "rect": {"x": 0, "y": 0, "width": 30, "height": 40}},
             ]
         }
     }
@@ -510,15 +494,11 @@ def test_default_min_cols_is_15_and_min_rows_is_0():
 
 
 def test_30_col_2_column_splitting_boundary():
-    """Verify width >= 30 cols allows 2-column splitting with default min_cols=15,
-    while width < 30 (e.g. 29) triggers column_width_overflow.
-    """
-    # 30 cols: 30 // 2 = 15 == min_cols(15) -> splits right
+    """N=1: width >= 30 allows a right split (min_cols=15); 29 overflows."""
     payload_30 = {
         "result": {
             "panes": [
-                {"pane_id": "p1", "rect": {"x": 0, "y": 0, "width": 30, "height": 20}},
-                {"pane_id": "p2", "rect": {"x": 0, "y": 20, "width": 30, "height": 20}},
+                {"pane_id": "p1", "rect": {"x": 0, "y": 0, "width": 30, "height": 40}},
             ]
         }
     }
@@ -526,12 +506,10 @@ def test_30_col_2_column_splitting_boundary():
     assert d30.direction == "right"
     assert not d30.is_overflow
 
-    # 29 cols: 29 // 2 = 14 < min_cols(15) -> overflow
     payload_29 = {
         "result": {
             "panes": [
-                {"pane_id": "p1", "rect": {"x": 0, "y": 0, "width": 29, "height": 20}},
-                {"pane_id": "p2", "rect": {"x": 0, "y": 20, "width": 29, "height": 20}},
+                {"pane_id": "p1", "rect": {"x": 0, "y": 0, "width": 29, "height": 40}},
             ]
         }
     }
@@ -542,51 +520,155 @@ def test_30_col_2_column_splitting_boundary():
 
 
 def test_54x23_compact_viewport_single_workspace_multi_pane_tiling():
-    """Verify complete 1 -> 2 -> 3 -> 4 pane tiling in standard 80x24 (54x23 content area) workspace.
-    - 1 pane (54x23): splits down to p1(54x11), p2(54x11)
-    - 2 panes: splits right (54//2 = 27 >= 15) to start col 2 -> p3(27x23)
-    - 3 panes: fills singleton col 2 down -> p4(27x11)
-    - 4 panes (2x2 grid): 5th agent overflows because 27 // 2 = 13 < 15
-    """
-    # 1 -> 2 (splits down)
+    """1→2 right, 2→3 down left, 3→4 down right, 4→5 overflow at capacity."""
     p1_layout = {"result": {"panes": [{"pane_id": "p1", "rect": {"x": 26, "y": 1, "width": 54, "height": 23}}]}}
     d1 = compute_2xk_layout(p1_layout)
-    assert d1.direction == "down"
+    assert d1.direction == "right"
     assert d1.target_pane_id == "p1"
     assert not d1.is_overflow
 
-    # 2 -> 3 (splits right)
     p2_layout = {"result": {"panes": [
-        {"pane_id": "p1", "rect": {"x": 26, "y": 1, "width": 54, "height": 11}},
-        {"pane_id": "p2", "rect": {"x": 26, "y": 12, "width": 54, "height": 11}},
+        {"pane_id": "p1", "rect": {"x": 26, "y": 1, "width": 27, "height": 23}},
+        {"pane_id": "p2", "rect": {"x": 53, "y": 1, "width": 27, "height": 23}},
     ]}}
     d2 = compute_2xk_layout(p2_layout)
-    assert d2.direction == "right"
+    assert d2.direction == "down"
     assert d2.target_pane_id == "p1"
     assert not d2.is_overflow
 
-    # 3 -> 4 (fills singleton col 2 down)
     p3_layout = {"result": {"panes": [
         {"pane_id": "p1", "rect": {"x": 26, "y": 1, "width": 27, "height": 11}},
-        {"pane_id": "p2", "rect": {"x": 26, "y": 12, "width": 27, "height": 11}},
-        {"pane_id": "p3", "rect": {"x": 53, "y": 1, "width": 27, "height": 23}},
+        {"pane_id": "p2", "rect": {"x": 53, "y": 1, "width": 27, "height": 23}},
+        {"pane_id": "p3", "rect": {"x": 26, "y": 12, "width": 27, "height": 12}},
     ]}}
     d3 = compute_2xk_layout(p3_layout)
     assert d3.direction == "down"
-    assert d3.target_pane_id == "p3"
+    assert d3.target_pane_id == "p2"
     assert not d3.is_overflow
 
-    # 4 -> 5 (overflow to new workspace because 27 // 2 = 13 < 15)
     p4_layout = {"result": {"panes": [
         {"pane_id": "p1", "rect": {"x": 26, "y": 1, "width": 27, "height": 11}},
-        {"pane_id": "p2", "rect": {"x": 26, "y": 12, "width": 27, "height": 11}},
-        {"pane_id": "p3", "rect": {"x": 53, "y": 1, "width": 27, "height": 11}},
-        {"pane_id": "p4", "rect": {"x": 53, "y": 12, "width": 27, "height": 11}},
+        {"pane_id": "p2", "rect": {"x": 53, "y": 1, "width": 27, "height": 11}},
+        {"pane_id": "p3", "rect": {"x": 26, "y": 12, "width": 27, "height": 12}},
+        {"pane_id": "p4", "rect": {"x": 53, "y": 12, "width": 27, "height": 12}},
     ]}}
     d4 = compute_2xk_layout(p4_layout)
     assert d4.direction == "overflow"
     assert d4.is_overflow
-    assert d4.reason == "column_width_overflow"
+    assert d4.reason == "grid_capacity_reached"
 
 
+def _payload(panes):
+    return {"result": {"panes": [
+        {"pane_id": p["id"], "rect": {"x": p["x"], "y": p["y"], "width": p["w"], "height": p["h"]}}
+        for p in panes
+    ]}}
+
+
+def _bsp_split(panes, tid, direction):
+    """herdr contract: bisect only the target pane's rect."""
+    out = []
+    next_id = f"p{len(panes) + 1}"
+    for p in panes:
+        if p["id"] != tid:
+            out.append(dict(p))
+            continue
+        if direction == "right":
+            w1 = p["w"] // 2
+            w2 = p["w"] - w1
+            out.append({**p, "w": w1})
+            out.append({"id": next_id, "x": p["x"] + w1, "y": p["y"], "w": w2, "h": p["h"]})
+        elif direction == "down":
+            h1 = p["h"] // 2
+            h2 = p["h"] - h1
+            out.append({**p, "h": h1})
+            out.append({"id": next_id, "x": p["x"], "y": p["y"] + h1, "w": p["w"], "h": h2})
+        else:
+            raise AssertionError(f"unexpected split {direction}")
+    return out
+
+
+def test_four_panes_form_clean_2x2():
+    panes = [{"id": "p1", "x": 0, "y": 0, "w": 277, "h": 78}]
+    for _ in range(3):
+        d = compute_2xk_layout(_payload(panes))
+        assert not d.is_overflow, d
+        panes = _bsp_split(panes, d.target_pane_id, d.direction)
+    assert len(panes) == 4
+    assert max(p["w"] for p in panes) - min(p["w"] for p in panes) <= 2
+    assert max(p["h"] for p in panes) - min(p["h"] for p in panes) <= 2
+
+
+def test_fifth_pane_overflows():
+    panes = [{"id": "p1", "x": 0, "y": 0, "w": 277, "h": 78}]
+    for _ in range(3):
+        d = compute_2xk_layout(_payload(panes))
+        assert not d.is_overflow
+        panes = _bsp_split(panes, d.target_pane_id, d.direction)
+    d = compute_2xk_layout(_payload(panes))
+    assert d.is_overflow and d.direction == "overflow"
+    assert d.reason == "grid_capacity_reached"
+
+
+@pytest.mark.parametrize("n,expected", [(1, "right"), (2, "down"), (3, "down"), (4, "overflow")])
+def test_headless_matches_gui_decision(n, expected):
+    hl = compute_2xk_layout(_headless(n), max_columns=2, max_rows=2)
+    assert hl.direction == expected, f"headless n={n}"
+
+
+def test_headless_gui_direction_parity_full_sequence():
+    panes = [{"id": "p1", "x": 0, "y": 0, "w": 277, "h": 78}]
+    for n in range(1, 5):
+        gui = compute_2xk_layout(_payload(panes), max_columns=2, max_rows=2)
+        hl = compute_2xk_layout(_headless(n), max_columns=2, max_rows=2)
+        assert gui.direction == hl.direction, f"divergence at n={n}"
+        if gui.is_overflow:
+            break
+        panes = _bsp_split(panes, gui.target_pane_id, gui.direction)
+
+
+def test_headless_fills_alternating_columns():
+    assert compute_2xk_layout(_headless(2), max_columns=2, max_rows=2).target_pane_id == "p1"
+    assert compute_2xk_layout(_headless(3), max_columns=2, max_rows=2).target_pane_id == "p2"
+
+
+def test_headless_ignores_sample_pane_anchor():
+    d = compute_2xk_layout(_headless(3), max_columns=2, max_rows=2, default_anchor_id="p1")
+    assert d.target_pane_id == "p2"
+
+
+def test_never_splits_right_on_partial_height_pane():
+    payload = {
+        "result": {
+            "panes": [
+                {"pane_id": "p1", "rect": {"x": 0, "y": 0, "width": 277, "height": 39}},
+                {"pane_id": "p2", "rect": {"x": 0, "y": 39, "width": 277, "height": 39}},
+            ]
+        }
+    }
+    d = compute_2xk_layout(payload, max_columns=2, max_rows=2)
+    assert d.direction != "right"
+
+
+def test_max_cols_default_reaches_cli_path():
+    payload = json.dumps(_four_panes_two_columns())
+    skills_dir = os.path.abspath(".agents/skills")
+    env = {**os.environ, "PYTHONPATH": skills_dir}
+    for k in _LAYOUT_ENV_VARS:
+        env.pop(k, None)
+    res = subprocess.run(
+        [sys.executable, "-m", "lib_py.layout", "--json"],
+        input=payload, capture_output=True, text=True, env=env)
+    assert res.returncode == 0, res.stderr
+    d = json.loads(res.stdout)
+    assert d["direction"] == "overflow"
+    assert d["reason"] == "grid_capacity_reached"
+
+
+def test_lib_sh_passes_max_cols_and_rows():
+    lib_path = os.path.abspath(".agents/skills/lib.sh")
+    content = open(lib_path, encoding="utf-8").read()
+    assert '--max-cols "${MAM_MAX_PANE_COLS:-2}"' in content
+    assert '--max-rows "${MAM_MAX_PANE_ROWS:-2}"' in content
+
 
diff --git a/tests/test_tier1_unit.py b/tests/test_tier1_unit.py
index ce99e53..0c5802e 100644
--- a/tests/test_tier1_unit.py
+++ b/tests/test_tier1_unit.py
@@ -872,12 +872,10 @@ def test_layout_default_min_cols_15_in_tier1():
     """Verify default min_cols=15 behavior across compute_2xk_layout in Tier 1 suite."""
     from lib_py.layout import compute_2xk_layout
 
-    # 1. 2 panes in 30 col width (30 // 2 = 15 == min_cols 15) -> splits right cleanly
     payload_30 = {
         "result": {
             "panes": [
-                {"pane_id": "p1", "rect": {"x": 0, "y": 0, "width": 30, "height": 20}},
-                {"pane_id": "p2", "rect": {"x": 0, "y": 20, "width": 30, "height": 20}}
+                {"pane_id": "p1", "rect": {"x": 0, "y": 0, "width": 30, "height": 40}},
             ]
         }
     }
@@ -886,12 +884,10 @@ def test_layout_default_min_cols_15_in_tier1():
     assert not decision.is_overflow
     assert decision.reason == "new_column_right"
 
-    # 2. 2 panes in 29 col width (29 // 2 = 14 < min_cols 15) -> column_width_overflow
     payload_29 = {
         "result": {
             "panes": [
-                {"pane_id": "p1", "rect": {"x": 0, "y": 0, "width": 29, "height": 20}},
-                {"pane_id": "p2", "rect": {"x": 0, "y": 20, "width": 29, "height": 20}}
+                {"pane_id": "p1", "rect": {"x": 0, "y": 0, "width": 29, "height": 40}},
             ]
         }
     }
@@ -905,45 +901,41 @@ def test_layout_single_workspace_54x23_compact_tiling_tier1():
     """Verify 3-4 agents tiling in standard 80x24 (54x23 content) terminal windows within a single workspace."""
     from lib_py.layout import compute_2xk_layout
 
-    # Step 1: 1 pane -> 2 panes (split down without height constraint)
     p1 = {"result": {"panes": [{"pane_id": "p1", "rect": {"x": 26, "y": 1, "width": 54, "height": 23}}]}}
     d1 = compute_2xk_layout(p1)
-    assert d1.direction == "down"
+    assert d1.direction == "right"
     assert d1.target_pane_id == "p1"
     assert not d1.is_overflow
 
-    # Step 2: 2 panes -> 3 panes (split right to open 2nd column)
     p2 = {"result": {"panes": [
-        {"pane_id": "p1", "rect": {"x": 26, "y": 1, "width": 54, "height": 11}},
-        {"pane_id": "p2", "rect": {"x": 26, "y": 12, "width": 54, "height": 11}}
+        {"pane_id": "p1", "rect": {"x": 26, "y": 1, "width": 27, "height": 23}},
+        {"pane_id": "p2", "rect": {"x": 53, "y": 1, "width": 27, "height": 23}}
     ]}}
     d2 = compute_2xk_layout(p2)
-    assert d2.direction == "right"
+    assert d2.direction == "down"
     assert d2.target_pane_id == "p1"
     assert not d2.is_overflow
 
-    # Step 3: 3 panes -> 4 panes (split singleton 2nd column down)
     p3 = {"result": {"panes": [
         {"pane_id": "p1", "rect": {"x": 26, "y": 1, "width": 27, "height": 11}},
-        {"pane_id": "p2", "rect": {"x": 26, "y": 12, "width": 27, "height": 11}},
-        {"pane_id": "p3", "rect": {"x": 53, "y": 1, "width": 27, "height": 23}}
+        {"pane_id": "p2", "rect": {"x": 53, "y": 1, "width": 27, "height": 23}},
+        {"pane_id": "p3", "rect": {"x": 26, "y": 12, "width": 27, "height": 12}}
     ]}}
     d3 = compute_2xk_layout(p3)
     assert d3.direction == "down"
-    assert d3.target_pane_id == "p3"
+    assert d3.target_pane_id == "p2"
     assert not d3.is_overflow
 
-    # Step 4: 4 panes (2x2 complete) -> 5th agent overflows to fresh workspace (27 // 2 = 13 < 15)
     p4 = {"result": {"panes": [
         {"pane_id": "p1", "rect": {"x": 26, "y": 1, "width": 27, "height": 11}},
-        {"pane_id": "p2", "rect": {"x": 26, "y": 12, "width": 27, "height": 11}},
-        {"pane_id": "p3", "rect": {"x": 53, "y": 1, "width": 27, "height": 11}},
-        {"pane_id": "p4", "rect": {"x": 53, "y": 12, "width": 27, "height": 11}}
+        {"pane_id": "p2", "rect": {"x": 53, "y": 1, "width": 27, "height": 11}},
+        {"pane_id": "p3", "rect": {"x": 26, "y": 12, "width": 27, "height": 12}},
+        {"pane_id": "p4", "rect": {"x": 53, "y": 12, "width": 27, "height": 12}}
     ]}}
     d4 = compute_2xk_layout(p4)
     assert d4.direction == "overflow"
     assert d4.is_overflow
-    assert d4.reason == "column_width_overflow"
+    assert d4.reason == "grid_capacity_reached"
 
 
 # ==============================================================================