diff --git a/src/tensor_layouts/analysis.py b/src/tensor_layouts/analysis.py
index 098089f..8c79511 100644
--- a/src/tensor_layouts/analysis.py
+++ b/src/tensor_layouts/analysis.py
@@ -114,7 +114,7 @@ def is_injective(layout: LayoutExpr) -> bool:
     return len(image(layout)) == size(layout)
 
 
-def is_surjective(layout: LayoutExpr, codomain_size: int = None) -> bool:
+def is_surjective(layout: LayoutExpr, codomain_size: int | None = None) -> bool:
     """True if every offset in [0, codomain_size) is produced.
 
     A surjective layout has no gaps --- the image covers the entire
@@ -131,9 +131,22 @@ def is_surjective(layout: LayoutExpr, codomain_size: int = None) -> bool:
         is_surjective(Layout(4, 1))    # True  (image == codomain)
         is_surjective(Layout(4, 2))    # False (image has gaps)
     """
+    offsets = image(layout)
     if codomain_size is None:
-        codomain_size = cosize(layout)
-    return len(image(layout)) == codomain_size
+        if not offsets:
+            return True
+        lo, hi = offsets[0], offsets[-1]
+        return len(offsets) == (hi - lo + 1)
+
+    if not is_int(codomain_size):
+        raise TypeError("codomain_size must be an integer")
+    if codomain_size < 0:
+        raise ValueError("codomain_size must be non-negative")
+    if codomain_size == 0:
+        return len(offsets) == 0
+    if len(offsets) != codomain_size:
+        return False
+    return offsets[0] == 0 and offsets[-1] == codomain_size - 1
 
 
 def is_bijective(layout: LayoutExpr) -> bool:
diff --git a/tests/analysis.py b/tests/analysis.py
index 8ed758a..6ce3a7f 100644
--- a/tests/analysis.py
+++ b/tests/analysis.py
@@ -1556,8 +1556,26 @@ def test_is_surjective_custom_codomain():
     layout = Layout(4, 2)
     # Not surjective onto [0, 7) -- has gaps
     assert not is_surjective(layout)
-    # Surjective if codomain is exactly the image size
-    assert is_surjective(layout, codomain_size=4)
+    # Still not surjective onto [0, 4) because the image is {0,2,4,6}
+    assert not is_surjective(layout, codomain_size=4)
+    # Surjective when codomain exactly matches requested range [0, 7)
+    assert is_surjective(Layout(7, 1), codomain_size=7)
+
+
+def test_is_surjective_custom_codomain_zero():
+    """codomain_size=0 is surjective only for empty images."""
+    assert is_surjective(Layout(0, 3), codomain_size=0)
+    assert not is_surjective(Layout(1, 0), codomain_size=0)
+
+
+def test_is_surjective_custom_codomain_validation():
+    """codomain_size must be a non-negative integer."""
+    with pytest.raises(TypeError):
+        is_surjective(Layout(4, 1), codomain_size=4.0)
+    with pytest.raises(TypeError):
+        is_surjective(Layout(4, 1), codomain_size=True)
+    with pytest.raises(ValueError):
+        is_surjective(Layout(4, 1), codomain_size=-1)
 
 
 def test_is_bijective_contiguous():
@@ -1597,6 +1615,12 @@ def test_is_bijective_negative_stride_dense():
     assert is_contiguous(layout)
 
 
+def test_is_surjective_negative_stride_custom_codomain():
+    """Negative-stride dense spans are not surjective onto [0, n) by default."""
+    layout = Layout(4, -1)
+    assert not is_surjective(layout, codomain_size=4)
+
+
 def test_image_injectivity_consistency():
     """image size equals domain size iff injective."""
     layouts = [