diff --git a/docs/whats-new.rst b/docs/whats-new.rst
index 48cebe3c..44e4733b 100644
--- a/docs/whats-new.rst
+++ b/docs/whats-new.rst
@@ -8,6 +8,8 @@ What's new
   By `Justus Magin <https://github.com/keewis>`_.
 - Don't rely on ``xarray``'s default behavior regarding ``attrs`` in :py:func:`pint_xarray.expects` (:issue:`360`, :pull:`367`)
   By `Justus Magin <https://github.com/keewis>`_.
+- Fix quantifying a existing index and adjust the index conversion tests (:pull:`368`)
+  By `Justus Magin <https://github.com/keewis>`_.
 
 0.6.0 (31 Aug 2025)
 -------------------
diff --git a/pint_xarray/conversion.py b/pint_xarray/conversion.py
index ecda7af3..4849b1d7 100644
--- a/pint_xarray/conversion.py
+++ b/pint_xarray/conversion.py
@@ -137,10 +137,13 @@ def attach_units_index(index, index_vars, units):
         # skip non-quantity indexed variables
         return index
 
-    if isinstance(index, PintIndex) and index.units != units:
-        raise ValueError(
-            f"cannot attach units to quantified index: {index.units} != {units}"
-        )
+    if isinstance(index, PintIndex):
+        if index.units != units:
+            raise ValueError(
+                f"cannot attach units to quantified index: {index.units} != {units}"
+            )
+        else:
+            return index
 
     return PintIndex(index=index, units=units)
 
diff --git a/pint_xarray/tests/test_conversion.py b/pint_xarray/tests/test_conversion.py
index f1d8dde0..057e6b18 100644
--- a/pint_xarray/tests/test_conversion.py
+++ b/pint_xarray/tests/test_conversion.py
@@ -418,11 +418,12 @@ def test_convert_units(self, type, variant, units, error, suberrors):
         expected_a = convert_quantity(q_a, units.get("a", original_units.get("a")))
         expected_b = convert_quantity(q_b, units.get("b", original_units.get("b")))
         expected_u = convert_quantity(q_u, units.get("u", original_units.get("u")))
-        expected_x = convert_quantity(q_x, units.get("x"))
+        expected_x = convert_quantity(q_x, units.get("x", original_units.get("x")))
         expected_index = PandasIndex(pd.Index(strip_quantity(expected_x)), "x")
-        if units.get("x") is not None:
+        expected_index_units = units.get("x", original_units.get("x"))
+        if expected_index_units is not None:
             expected_index = PintIndex(
-                index=expected_index, units={"x": units.get("x")}
+                index=expected_index, units={"x": expected_index_units}
             )
 
         expected = Dataset(