diff --git a/django/db/models/base.py b/django/db/models/base.py
index c96507d5a1..c7c62ea367 100644
--- a/django/db/models/base.py
+++ b/django/db/models/base.py
@@ -450,11 +450,6 @@ class Model(six.with_metaclass(ModelBase)):
 
     def __str__(self):
         if six.PY2 and hasattr(self, '__unicode__'):
-            if type(self).__unicode__ == Model.__str__:
-                klass_name = type(self).__name__
-                raise RuntimeError("%s.__unicode__ is aliased to __str__. Did"
-                                   " you apply @python_2_unicode_compatible"
-                                   " without defining __str__?" % klass_name)
             return force_text(self).encode('utf-8')
         return '%s object' % self.__class__.__name__
 
diff --git a/django/utils/encoding.py b/django/utils/encoding.py
index bb07deb894..6d1d575faf 100644
--- a/django/utils/encoding.py
+++ b/django/utils/encoding.py
@@ -28,6 +28,10 @@ def python_2_unicode_compatible(klass):
     returning text and apply this decorator to the class.
     """
     if six.PY2:
+        if '__str__' not in klass.__dict__:
+            raise ValueError("@python_2_unicode_compatible cannot be applied "
+                             "to %s because it doesn't define __str__()." %
+                             klass.__name__)
         klass.__unicode__ = klass.__str__
         klass.__str__ = lambda self: self.__unicode__().encode('utf-8')
     return klass
diff --git a/tests/commands_sql/models.py b/tests/commands_sql/models.py
index d8f372b403..78ad722307 100644
--- a/tests/commands_sql/models.py
+++ b/tests/commands_sql/models.py
@@ -1,13 +1,10 @@
 from django.db import models
-from django.utils.encoding import python_2_unicode_compatible
 
 
-@python_2_unicode_compatible
 class Comment(models.Model):
     pass
 
 
-@python_2_unicode_compatible
 class Book(models.Model):
     title = models.CharField(max_length=100, db_index=True)
     comments = models.ManyToManyField(Comment)
diff --git a/tests/str/models.py b/tests/str/models.py
index 1c158ea008..488012e861 100644
--- a/tests/str/models.py
+++ b/tests/str/models.py
@@ -27,14 +27,6 @@ class Article(models.Model):
         # in ASCII.
         return self.headline
 
-@python_2_unicode_compatible
-class BrokenArticle(models.Model):
-    headline = models.CharField(max_length=100)
-    pub_date = models.DateTimeField()
-
-    def __unicode__(self):      # instead of __str__
-        return self.headline
-
 @python_2_unicode_compatible
 class InternationalArticle(models.Model):
     headline = models.CharField(max_length=100)
diff --git a/tests/str/tests.py b/tests/str/tests.py
index 3c0bc079c8..aeb2874195 100644
--- a/tests/str/tests.py
+++ b/tests/str/tests.py
@@ -7,7 +7,7 @@ from unittest import skipIf
 from django.test import TestCase
 from django.utils import six
 
-from .models import Article, BrokenArticle, InternationalArticle
+from .models import Article, InternationalArticle
 
 
 class SimpleTests(TestCase):
@@ -21,16 +21,6 @@ class SimpleTests(TestCase):
         self.assertEqual(str(a), str('Area man programs in Python'))
         self.assertEqual(repr(a), str('<Article: Area man programs in Python>'))
 
-    @skipIf(six.PY3, "tests Model's default __str__ method under Python 2")
-    def test_broken(self):
-        # Regression test for #19362.
-        a = BrokenArticle.objects.create(
-            headline='Girl wins €12.500 in lottery',
-            pub_date=datetime.datetime(2005, 7, 28)
-        )
-        six.assertRaisesRegex(self, RuntimeError, "Did you apply "
-            "@python_2_unicode_compatible without defining __str__\?", str, a)
-
     def test_international(self):
         a = InternationalArticle.objects.create(
             headline='Girl wins €12.500 in lottery',
diff --git a/tests/utils_tests/test_encoding.py b/tests/utils_tests/test_encoding.py
index 81a4c4f5da..a91f5965db 100644
--- a/tests/utils_tests/test_encoding.py
+++ b/tests/utils_tests/test_encoding.py
@@ -5,7 +5,8 @@ import unittest
 import datetime
 
 from django.utils import six
-from django.utils.encoding import force_bytes, force_text, filepath_to_uri
+from django.utils.encoding import (force_bytes, force_text, filepath_to_uri,
+        python_2_unicode_compatible)
 
 
 class TestEncodingUtils(unittest.TestCase):
@@ -43,3 +44,10 @@ class TestEncodingUtils(unittest.TestCase):
             'upload/%D1%87%D1%83%D0%B1%D0%B0%D0%BA%D0%B0.mp4')
         self.assertEqual(filepath_to_uri('upload\\чубака.mp4'.encode('utf-8')),
             'upload/%D1%87%D1%83%D0%B1%D0%B0%D0%BA%D0%B0.mp4')
+
+    @unittest.skipIf(six.PY3, "tests a class not defining __str__ under Python 2")
+    def test_decorated_class_without_str(self):
+        with self.assertRaises(ValueError):
+            @python_2_unicode_compatible
+            class NoStr(object):
+                pass