diff --git a/cfgrib/dataset.py b/cfgrib/dataset.py
index 1dbe3f09..cea3f810 100644
--- a/cfgrib/dataset.py
+++ b/cfgrib/dataset.py
@@ -521,13 +521,18 @@ def build_variable_components(
     extra_coords_data: T.Dict[str, T.Dict[str, T.Any]] = {
         coord_name: {} for coord_name in extra_coords
     }
-    for dim in header_dimensions:
-        header_value_index[dim] = {v: i for i, v in enumerate(coord_vars[dim].data.tolist())}
+    extra_dims = tuple(extra_coords.values())
+    for dim in header_dimensions + extra_dims:
+        if np.isscalar(coord_vars[dim].data):
+            header_value_index[dim] = {np.asscalar(coord_vars[dim].data): 0}
+        else:
+            header_value_index[dim] = {v: i for i, v in enumerate(coord_vars[dim].data.tolist())}
     for header_values, offset in index.offsets:
         header_indexes = []  # type: T.List[int]
-        for dim in header_dimensions:
+        for dim in header_dimensions + extra_dims:
             header_value = header_values[index.index_keys.index(coord_name_key_map.get(dim, dim))]
-            header_indexes.append(header_value_index[dim][header_value])
+            if dim in header_dimensions:
+                header_indexes.append(header_value_index[dim][header_value])
             for coord_name in extra_coords:
                 coord_value = header_values[
                     index.index_keys.index(coord_name_key_map.get(coord_name, coord_name))
@@ -563,10 +568,14 @@ def build_variable_components(
         coord_vars["valid_time"] = Variable(dimensions=time_dims, data=time_data, attributes=attrs)
 
     for coord_name in extra_coords:
-        coord_vars[coord_name] = Variable(
-            dimensions=(extra_coords[coord_name],),
-            data=np.array(list(extra_coords_data[coord_name].values())),
-        )
+        coord_data = np.array(list(extra_coords_data[coord_name].values()))
+        if extra_coords[coord_name] not in header_dimensions:
+            coord_dimensions: T.Tuple[str, ...] = ()
+            coord_data = coord_data.reshape(())
+        else:
+            coord_dimensions = (extra_coords[coord_name],)
+        coord_vars[coord_name] = Variable(dimensions=coord_dimensions, data=coord_data,)
+
     data_var_attrs["coordinates"] = " ".join(coord_vars.keys())
     # OnDiskArray is close enough to np.ndarray to work, but not to make mypy happy
     data_var = Variable(dimensions=dimensions, data=on_disk_array, attributes=data_var_attrs)  # type: ignore
diff --git a/cfgrib/xarray_plugin.py b/cfgrib/xarray_plugin.py
index 74b5aea8..474514f4 100644
--- a/cfgrib/xarray_plugin.py
+++ b/cfgrib/xarray_plugin.py
@@ -94,6 +94,7 @@ def open_dataset(
         squeeze: bool = True,
         time_dims: T.Iterable[str] = ("time", "step"),
         errors: str = "warn",
+        extra_coords: T.Dict[str, str] = {},
     ) -> xr.Dataset:
 
         store = CfGribDataStore(
@@ -106,6 +107,7 @@ def open_dataset(
             time_dims=time_dims,
             lock=lock,
             errors=errors,
+            extra_coords=extra_coords,
         )
         with xr.core.utils.close_on_error(store):
             vars, attrs = store.load()  # type: ignore
diff --git a/tests/sample-data/era5-single-level-scalar-time.grib b/tests/sample-data/era5-single-level-scalar-time.grib
new file mode 100644
index 00000000..8ca53650
Binary files /dev/null and b/tests/sample-data/era5-single-level-scalar-time.grib differ
diff --git a/tests/test_30_dataset.py b/tests/test_30_dataset.py
index 36b9f9b7..57d5fd92 100644
--- a/tests/test_30_dataset.py
+++ b/tests/test_30_dataset.py
@@ -9,6 +9,7 @@
 SAMPLE_DATA_FOLDER = os.path.join(os.path.dirname(__file__), "sample-data")
 TEST_DATA = os.path.join(SAMPLE_DATA_FOLDER, "era5-levels-members.grib")
 TEST_DATA_UKMO = os.path.join(SAMPLE_DATA_FOLDER, "forecast_monthly_ukmo.grib")
+TEST_DATA_SCALAR_TIME = os.path.join(SAMPLE_DATA_FOLDER, "era5-single-level-scalar-time.grib")
 
 
 def test_enforce_unique_attributes():
@@ -206,7 +207,15 @@ def test_Dataset_extra_coords():
     assert res.variables["experimentVersionNumber"].dimensions == ("time",)
 
 
-def test_Dataet_extra_coords_error():
+def test_Dataset_scalar_extra_coords():
+    res = dataset.open_file(
+        TEST_DATA_SCALAR_TIME, extra_coords={"experimentVersionNumber": "time"}
+    )
+    assert "experimentVersionNumber" in res.variables
+    assert res.variables["experimentVersionNumber"].dimensions == ()
+
+
+def test_Dataset_extra_coords_error():
     with pytest.raises(ValueError):
         dataset.open_file(TEST_DATA, extra_coords={"validityDate": "number"})
 
diff --git a/tests/test_50_sample_data.py b/tests/test_50_sample_data.py
index b7149637..a99417de 100644
--- a/tests/test_50_sample_data.py
+++ b/tests/test_50_sample_data.py
@@ -89,3 +89,17 @@ def test_canonical_dataset_to_grib(grib_name, tmpdir):
         xarray_to_grib.canonical_dataset_to_grib(res, out_path)
     reread = xarray_store.open_dataset(out_path)
     assert res.equals(reread)
+
+
+@pytest.mark.parametrize(
+    "grib_name,ndims", [("era5-levels-members", 1), ("era5-single-level-scalar-time", 0),],
+)
+def test_open_dataset_extra_coords(grib_name, ndims):
+    grib_path = os.path.join(SAMPLE_DATA_FOLDER, grib_name + ".grib")
+    res = xarray_store.open_dataset(
+        grib_path,
+        backend_kwargs={"extra_coords": {"experimentVersionNumber": "time"}},
+        cache=False,
+    )
+    assert "experimentVersionNumber" in res.coords
+    assert len(res["experimentVersionNumber"].dims) == ndims