diff --git a/CHANGES.rst b/CHANGES.rst
index cf6c99b3..fd02ca5f 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -1,6 +1,10 @@
 What's new
 ==========
 
+0.8.4 (2024-02-26)
+------------------
+* Fix regression from :pull:`332` that made ``Regridder`` fail with rectilinear datasets and ``parallel=True``. (:issue:`343`, :pull:`344`).
+
 0.8.3 (2024-02-20)
 ------------------
 * Remove usage of private method of xarray that was removed in its 2024.02.0 version (:issue:`338`, :issue:`340`) By `Pascal Bourgault <https://github.com/aulemahal>`_.
@@ -9,7 +13,6 @@ Internal changes
 ----------------
 * Test against ESMF 8.6
 
-
 0.8.2 (2023-09-18)
 ------------------
 
@@ -18,10 +21,6 @@ Bug fixes
 * Raise a meaningful error messages when the output grid has no chunks with `parallel=True` (:issue:`299`, :pull:`304`). By `Pascal Bourgault <https://github.com/aulemahal>`_.
 * Correct guess of output chunks for ``SpatialAverager``.
 
-Internal changes
-----------------
-* Test against ESMF 8.6
-
 0.8.1 (2023-09-05)
 ------------------
 
diff --git a/xesmf/frontend.py b/xesmf/frontend.py
index 6b8f1a1d..cf6f30e1 100644
--- a/xesmf/frontend.py
+++ b/xesmf/frontend.py
@@ -1031,7 +1031,9 @@ def _init_para_regrid(self, ds_in, ds_out, kwargs):
 
         # Rename coords to avoid issues in xr.map_blocks
         for coord in list(self.out_coords.keys()):
-            ds_out = ds_out.rename({coord: coord + '_out'})
+            # If coords and dims are the same, renaming has already been done.
+            if coord not in self.out_horiz_dims:
+                ds_out = ds_out.rename({coord: coord + '_out'})
 
         weights_dims = ('y_out', 'x_out', 'y_in', 'x_in')
         templ = sps.zeros((self.shape_out + self.shape_in))
diff --git a/xesmf/tests/test_frontend.py b/xesmf/tests/test_frontend.py
index 0d0b9d81..2c9e52b3 100644
--- a/xesmf/tests/test_frontend.py
+++ b/xesmf/tests/test_frontend.py
@@ -634,6 +634,21 @@ def test_para_weight_gen():
     # weights should be identical between serial and parallel
     assert all(regridder.w.data.data == para_regridder.w.data.data)
 
+    # Should work with a rectilinear version too (where dims == coords)
+    ds_in_cf = xe.util.cf_grid_2d(-90, 90, 20, -45, 45, 12)
+    ds_out_cf = xe.util.cf_grid_2d(-90, 90, 15, -45, 45, 9)
+    ds_in_cf['data'] = xe.data.wave_smooth(ds_in_cf['lon'], ds_in_cf['lat'])
+    ds_out_cf['data_ref'] = xe.data.wave_smooth(ds_out_cf['lon'], ds_out_cf['lat']).chunk(
+        {'lat': 5, 'lon': 5}
+    )
+
+    # Generating weights in serial and parallel
+    regridder = xe.Regridder(ds_in_cf, ds_out_cf, 'conservative')
+    para_regridder = xe.Regridder(ds_in_cf, ds_out_cf, 'conservative', parallel=True)
+
+    # weights should be identical between serial and parallel
+    assert all(regridder.w.data.data == para_regridder.w.data.data)
+
     # Ensure para weight gen works with locstream_in as well
     reggrider_locs = xe.Regridder(ds_locs, ds_out_chunked, 'nearest_s2d', locstream_in=True)
     para_regridder_locs = xe.Regridder(