diff --git a/taggit/models.py b/taggit/models.py
index 091d733b..823eb362 100644
--- a/taggit/models.py
+++ b/taggit/models.py
@@ -9,9 +9,20 @@
 
 try:
     from unidecode import unidecode
+
+    unidecode_installed = True
 except ImportError:
+    unidecode_installed = False
+
 
-    def unidecode(tag):
+def slugify_unicode_stripping_prep(tag):
+    """
+    This handles stripping via unidecode if it's installed,
+    otherwise is a no-op
+    """
+    if unidecode_installed:
+        return unidecode(tag)
+    else:
         return tag
 
 
@@ -97,7 +108,7 @@ def save(self, *args, **kwargs):
 
     def slugify(self, tag, i=None):
         if getattr(settings, "TAGGIT_STRIP_UNICODE_WHEN_SLUGIFYING", False):
-            slug = slugify(unidecode(tag))
+            slug = slugify(slugify_unicode_stripping_prep(tag))
         else:
             slug = slugify(tag, allow_unicode=True)
         if i is not None:
diff --git a/tests/test_models.py b/tests/test_models.py
index 4a9b748c..9f08d32c 100644
--- a/tests/test_models.py
+++ b/tests/test_models.py
@@ -1,5 +1,9 @@
+from unittest import skipIf
+
 from django.test import TestCase, override_settings
 
+from taggit import models as taggit_models
+
 from tests.models import TestModel
 
 
@@ -22,7 +26,30 @@ def test_unicode_slugs(self):
         sample_obj.tags.add("あい うえお")
         self.assertEqual([tag.slug for tag in sample_obj.tags.all()], ["あい-うえお"])
 
-    def test_old_slugs(self):
+    def test_old_slugs_wo_unidecode(self):
+        """
+        Test that the setting that gives us the old slugification behavior
+        is in place
+        """
+        with override_settings(TAGGIT_STRIP_UNICODE_WHEN_SLUGIFYING=True):
+            old_installed_value = taggit_models.unidecode_installed
+            taggit_models.unidecode_installed = False
+            try:
+                sample_obj = TestModel.objects.create()
+                # a unicode tag will be slugified for space reasons but
+                # unicode-ness will be kept by default
+                sample_obj.tags.add("あい うえお")
+                self.assertEqual(
+                    [tag.slug for tag in sample_obj.tags.all()], ["ai-ueo"]
+                )
+            finally:
+                taggit_models.unidecode_installed = old_installed_value
+
+    @skipIf(
+        not taggit_models.unidecode_installed,
+        "This test requires unidecode to be installed",
+    )
+    def test_old_slugs_with_unidecode(self):
         """
         Test that the setting that gives us the old slugification behavior
         is in place
diff --git a/tox.ini b/tox.ini
index d3152f08..6db8634b 100644
--- a/tox.ini
+++ b/tox.ini
@@ -25,6 +25,7 @@ deps =
     djmain: https://github.com/django/django/archive/main.tar.gz
     coverage
     djangorestframework
+    unidecode
 setenv =
     PYTHONWARNINGS=all
 commands =