diff --git a/tests/test_regrid/test_regridder.py b/tests/test_regrid/test_regridder.py
index 699e39fd..515881ee 100644
--- a/tests/test_regrid/test_regridder.py
+++ b/tests/test_regrid/test_regridder.py
@@ -283,3 +283,41 @@ def test_create_percentile_method():
     weights = np.ones_like(values)
     workspace = np.zeros_like(values)
     assert median(values, weights, workspace) == 2
+
+
+def test_directional_dependence():
+    # Increasing / decreasing x or y direction shouldn't matter for the result.
+    da = xr.DataArray(
+        data=[[1.0, 2.0], [3.0, 4.0]],
+        coords={"y": [17.5, 12.5], "x": [2.5, 7.5]},
+        dims=("y", "x"),
+    )
+    target_da = xr.DataArray(
+        data=[[np.nan, np.nan], [np.nan, np.nan]],
+        coords={"y": [10.0, 20.0], "x": [0.0, 10.0]},
+        dims=("y", "x"),
+    )
+    target_uda = xu.UgridDataArray.from_structured(target_da)
+
+    flip = slice(None, None, -1)
+    flipy = da.isel(y=flip)
+    flipx = da.isel(x=flip)
+    flipxy = da.isel(x=flip, y=flip)
+    uda = xu.UgridDataArray.from_structured(da)
+    uda_flipxy = xu.UgridDataArray.from_structured(flipxy)
+
+    # Structured target: test whether the result is the same regardless of source
+    # orientation.
+    result = []
+    for source in [da, flipy, flipx, flipxy, uda, uda_flipxy]:
+        regridder = xu.OverlapRegridder(source, taget=target_da)
+        result.append(regridder.regrid(source))
+    assert all(result[0] == item for item in result[1:])
+
+    # Unstructured target: test whether the result is the same regardless of
+    # source orientation.
+    result = []
+    for source in [da, flipy, flipx, flipxy, uda, uda_flipxy]:
+        regridder = xu.OverlapRegridder(source, taget=target_uda)
+        result.append(regridder.regrid(source))
+    assert all(result[0] == item for item in result[1:])
diff --git a/tests/test_regrid/test_structured.py b/tests/test_regrid/test_structured.py
index b5006a77..ca6e8db9 100644
--- a/tests/test_regrid/test_structured.py
+++ b/tests/test_regrid/test_structured.py
@@ -1,5 +1,6 @@
 import numpy as np
 import pytest
+import xarray as xr
 
 from xugrid.regrid.structured import StructuredGrid1d, StructuredGrid2d
 
@@ -404,3 +405,25 @@ def test_linear_weights_2d(
         np.array([5, 5, 5, 5, 6, 6, 6, 6, 9, 9, 9, 9, 10, 10, 10, 10]),
         np.array([1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0]),
     )
+
+
+def test_nonscalar_dx():
+    da = xr.DataArray(
+        [1, 2, 3], coords={"x": [1, 2, 3], "dx": ("x", [1, 1, 1])}, dims=("x",)
+    )
+    grid = StructuredGrid1d(da, name="x")
+    actual = xr.DataArray([1, 2, 3], coords=grid.coords, dims=grid.dims)
+    assert actual.identical(da)
+
+
+def test_directional_bounds():
+    da = xr.DataArray([1, 2, 3], coords={"y": [1, 2, 3]}, dims=("y",))
+    decreasing = da.isel(y=slice(None, None, -1))
+    grid_inc = StructuredGrid1d(da, name="y")
+    grid_dec = StructuredGrid1d(decreasing, name="y")
+    assert grid_inc.flipped is False
+    assert grid_dec.flipped is True
+    assert np.array_equal(grid_inc.bounds, grid_dec.bounds)
+    assert np.array_equal(
+        grid_inc.directional_bounds, grid_dec.directional_bounds[::-1]
+    )
diff --git a/xugrid/regrid/structured.py b/xugrid/regrid/structured.py
index 20e1ee1b..c670810a 100644
--- a/xugrid/regrid/structured.py
+++ b/xugrid/regrid/structured.py
@@ -83,10 +83,12 @@ def __init__(self, obj: Union[xr.DataArray, xr.Dataset], name: str):
 
     @property
     def coords(self) -> dict:
-        return {
-            self.name: self.index,
-            self.dname: self.dvalue,
-        }
+        coords = {self.name: self.index}
+        if isinstance(self.dvalue, np.ndarray):
+            coords[self.dname] = (self.name, self.dvalue)
+        else:
+            coords[self.dname] = self.dvalue
+        return coords
 
     @property
     def ndim(self) -> int:
@@ -104,6 +106,14 @@ def size(self) -> int:
     def length(self) -> FloatArray:
         return np.squeeze(abs(np.diff(self.bounds, axis=1)))
 
+    @property
+    def directional_bounds(self):
+        # Only flip bounds if needed
+        if self.flipped:
+            return self.bounds[::-1, :].copy()
+        else:
+            return self.bounds
+
     def flip_if_needed(self, index: IntArray) -> IntArray:
         if self.flipped:
             return self.size - index - 1
@@ -462,8 +472,8 @@ def convert_to(self, matched_type: Any) -> Any:
             return self
         elif matched_type == UnstructuredGrid2d:
             ugrid2d = Ugrid2d.from_structured_bounds(
-                self.xbounds.bounds,
-                self.ybounds.bounds,
+                self.xbounds.directional_bounds,
+                self.ybounds.directional_bounds,
             )
             return UnstructuredGrid2d(ugrid2d)
         else: