diff --git a/babel/units.py b/babel/units.py
index 0f32014aa..52fc56a41 100644
--- a/babel/units.py
+++ b/babel/units.py
@@ -88,6 +88,7 @@ def _find_unit_pattern(unit_id: str, locale: Locale | str | None = None) -> str
         )
         if new_id in unit_patterns:
             return new_id
+        unit_id = new_id
 
     # ... and finally fuzzy matching.
     for unit_pattern in sorted(unit_patterns, key=len):
diff --git a/tests/test_units.py b/tests/test_units.py
index dcb938775..9a6fd6035 100644
--- a/tests/test_units.py
+++ b/tests/test_units.py
@@ -1,6 +1,8 @@
+from functools import partial
+
 import pytest
 
-from babel.units import format_unit, get_unit_name
+from babel.units import _DEPRECATED_UNIT_IDS, format_unit, get_unit_name
 
 
 # New units in CLDR 46
@@ -37,10 +39,13 @@ def test_issue_1217(count, unit, locale, length, expected):
     assert format_unit(count, unit, length, locale=locale) == expected
 
 
-def test_deprecated_unit_ids():
-    for id in ("concentr-permillion", "concentr-portion", "concentr-portion-per-1e9"):
-        with pytest.warns(DeprecationWarning, match=id):
-            format_unit(1, id, locale='en')
+@pytest.mark.parametrize(('unit_id', 'replacement'), _DEPRECATED_UNIT_IDS.items())
+def test_deprecated_unit_ids(unit_id, replacement):
+    for func in (partial(format_unit, 1), get_unit_name):
+        with pytest.warns(DeprecationWarning, match=unit_id) as record:
+            result = func(unit_id, locale='en')
+        assert len(record) == 1
+        assert result == func(replacement, locale='en')
 
 
 @pytest.mark.parametrize(