diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 9d2981d098d..1d7c425e554 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -38,6 +38,10 @@ Bug fixes
   checking. (:issue:`3779`, :pull:`3787`)
   By `Justus Magin <https://github.com/keewis>`_.
 
+- :py:func:`concat` can now handle coordinate variables only present in one of
+  the objects to be concatenated when ``coords="different"``.
+  By `Deepak Cherian <https://github.com/dcherian>`_.
+
 Documentation
 ~~~~~~~~~~~~~
 
diff --git a/xarray/core/concat.py b/xarray/core/concat.py
index 302f7afcec6..96b4be15d1b 100644
--- a/xarray/core/concat.py
+++ b/xarray/core/concat.py
@@ -194,7 +194,23 @@ def process_subset_opt(opt, subset):
                 for k in getattr(datasets[0], subset):
                     if k not in concat_over:
                         equals[k] = None
-                        variables = [ds.variables[k] for ds in datasets]
+
+                        variables = []
+                        for ds in datasets:
+                            if k in ds.variables:
+                                variables.append(ds.variables[k])
+
+                        if len(variables) == 1:
+                            # coords="different" doesn't make sense when only one object
+                            # contains a particular variable.
+                            break
+                        elif len(variables) != len(datasets) and opt == "different":
+                            raise ValueError(
+                                f"{k!r} not present in all datasets and coords='different'. "
+                                f"Either add {k!r} to datasets where it is missing or "
+                                "specify coords='minimal'."
+                            )
+
                         # first check without comparing values i.e. no computes
                         for var in variables[1:]:
                             equals[k] = getattr(variables[0], compat)(
diff --git a/xarray/tests/test_combine.py b/xarray/tests/test_combine.py
index d907e1c5e46..eb2c6e1dbf7 100644
--- a/xarray/tests/test_combine.py
+++ b/xarray/tests/test_combine.py
@@ -365,9 +365,10 @@ def test_nested_concat(self):
         expected = Dataset({"x": ("a", [0, 1]), "y": ("a", [0, 1])})
         assert_identical(expected, actual)
 
-        objs = [Dataset({"x": [0], "y": [0]}), Dataset({"x": [0]})]
-        with pytest.raises(KeyError):
-            combine_nested(objs, concat_dim="x")
+        objs = [Dataset({"x": [0], "y": [0]}), Dataset({"x": [1]})]
+        actual = combine_nested(objs, concat_dim="x")
+        expected = Dataset({"x": [0, 1], "y": [0]})
+        assert_identical(expected, actual)
 
     @pytest.mark.parametrize(
         "join, expected",
diff --git a/xarray/tests/test_concat.py b/xarray/tests/test_concat.py
index def5abc942f..bd99181a947 100644
--- a/xarray/tests/test_concat.py
+++ b/xarray/tests/test_concat.py
@@ -475,3 +475,24 @@ def test_concat_attrs_first_variable(attr1, attr2):
 
     concat_attrs = concat(arrs, "y").attrs
     assert concat_attrs == attr1
+
+
+def test_concat_merge_single_non_dim_coord():
+    da1 = DataArray([1, 2, 3], dims="x", coords={"x": [1, 2, 3], "y": 1})
+    da2 = DataArray([4, 5, 6], dims="x", coords={"x": [4, 5, 6]})
+
+    expected = DataArray(range(1, 7), dims="x", coords={"x": range(1, 7), "y": 1})
+
+    for coords in ["different", "minimal"]:
+        actual = concat([da1, da2], "x", coords=coords)
+        assert_identical(actual, expected)
+
+    with raises_regex(ValueError, "'y' is not present in all datasets."):
+        concat([da1, da2], dim="x", coords="all")
+
+    da1 = DataArray([1, 2, 3], dims="x", coords={"x": [1, 2, 3], "y": 1})
+    da2 = DataArray([4, 5, 6], dims="x", coords={"x": [4, 5, 6]})
+    da3 = DataArray([7, 8, 9], dims="x", coords={"x": [7, 8, 9], "y": 1})
+    for coords in ["different", "all"]:
+        with raises_regex(ValueError, "'y' not present in all datasets"):
+            concat([da1, da2, da3], dim="x")