diff --git a/CHANGELOG.md b/CHANGELOG.md
index 3bc752f12..fda2167a4 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -5,6 +5,9 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 ## [Unreleased]
 
+### Added
+- `TopologyDesignRegion` is now invariant in `z` by default and supports assigning dimensions along which a design should be uniform via `TopologyDesignRegion(uniform=(bool, bool, bool))`.
+
 ### Fixed
 - Some validation fixes for design region.
 
diff --git a/tests/test_plugins/test_invdes.py b/tests/test_plugins/test_invdes.py
index 814fcb983..2088a0479 100644
--- a/tests/test_plugins/test_invdes.py
+++ b/tests/test_plugins/test_invdes.py
@@ -95,6 +95,18 @@ def test_region_params():
     _ = design_region.params_zeros
 
 
+def test_region_uniform():
+    """Test parameter shape for uniform dimensions"""
+    region = make_design_region()
+    shape = region.params_shape
+
+    test_region = region.updated_copy(uniform=(1, 1, 1))
+    assert test_region.params_shape == (1, 1, 1)
+
+    test_region = region.updated_copy(uniform=(1, 0, 1))
+    assert test_region.params_shape == (1, *shape[1:])
+
+
 def test_region_penalties():
     """Test evaluation of penalties of a ``TopologyDesignRegion``."""
 
diff --git a/tidy3d/plugins/invdes/region.py b/tidy3d/plugins/invdes/region.py
index 543adf658..5c60261c0 100644
--- a/tidy3d/plugins/invdes/region.py
+++ b/tidy3d/plugins/invdes/region.py
@@ -124,6 +124,13 @@ class TopologyDesignRegion(DesignRegion):
         "a value on the same order as the grid size.",
     )
 
+    uniform: tuple[bool, bool, bool] = pd.Field(
+        (False, False, True),
+        title="Uniform",
+        description="Axes along which the design should be uniform. By default, the structure "
+        "is assumed to be uniform, i.e. invariant, in the z direction.",
+    )
+
     transformations: typing.Tuple[TransformationType, ...] = pd.Field(
         (),
         title="Transformations",
@@ -166,12 +173,10 @@ def _check_params(params: anp.ndarray = None):
     @property
     def params_shape(self) -> typing.Tuple[int, int, int]:
         """Shape of the parameters array in (x, y, z), given the ``pixel_size`` and bounds."""
-        # rmin, rmax = np.array(self.geometry.bounds)
-        # lengths = rmax - rmin
         side_lengths = np.array(self.size)
         num_pixels = np.ceil(side_lengths / self.pixel_size)
         # TODO: if the structure is infinite but the simulation is finite, need reduced bounds
-        num_pixels[np.isinf(num_pixels)] = 1
+        num_pixels[np.logical_or(np.isinf(num_pixels), self.uniform)] = 1
         return tuple(int(n) for n in num_pixels)
 
     def _warn_deprecate_params(self):