diff --git a/docs/api-guide/routers.md b/docs/api-guide/routers.md
index 7efc140a5..d18ffbc82 100644
--- a/docs/api-guide/routers.md
+++ b/docs/api-guide/routers.md
@@ -90,6 +90,12 @@ This behavior can be modified by setting the `trailing_slash` argument to `False
 
 Trailing slashes are conventional in Django, but are not used by default in some other frameworks such as Rails.  Which style you choose to use is largely a matter of preference, although some javascript frameworks may expect a particular routing style.
 
+With `trailing_slash` set to True, the router will match lookup values containing any characters except slashes and dots. When set to False, dots are allowed.  To restrict the lookup pattern, set the `lookup_field_regex` attribute on the viewset.  For example, you can limit the lookup to valid UUIDs:
+
+    class MyModelViewSet(mixins.RetrieveModelMixin, viewsets.GenericViewSet):
+        lookup_field = 'my_model_id'
+        lookup_value_regex = '[0-9a-f]{32}'
+
 ## DefaultRouter
 
 This router is similar to `SimpleRouter` as above, but additionally includes a default API root view, that returns a response containing hyperlinks to all the list views.  It also generates routes for optional `.json` style format suffixes.
diff --git a/rest_framework/routers.py b/rest_framework/routers.py
index 97b35c10a..8cd98c863 100644
--- a/rest_framework/routers.py
+++ b/rest_framework/routers.py
@@ -195,13 +195,21 @@ class SimpleRouter(BaseRouter):
 
         https://github.com/alanjds/drf-nested-routers
         """
-        if self.trailing_slash:
-            base_regex = '(?P<{lookup_prefix}{lookup_field}>[^/]+)'
-        else:
-            # Don't consume `.json` style suffixes
-            base_regex = '(?P<{lookup_prefix}{lookup_field}>[^/.]+)'
+        base_regex = '(?P<{lookup_prefix}{lookup_field}>{lookup_value})'
         lookup_field = getattr(viewset, 'lookup_field', 'pk')
-        return base_regex.format(lookup_field=lookup_field, lookup_prefix=lookup_prefix)
+        try:
+            lookup_value = viewset.lookup_value_regex
+        except AttributeError:
+            if self.trailing_slash:
+                lookup_value = '[^/]+'
+            else:
+                # Don't consume `.json` style suffixes
+                lookup_value = '[^/.]+'
+        return base_regex.format(
+            lookup_prefix=lookup_prefix,
+            lookup_field=lookup_field,
+            lookup_value=lookup_value
+        )
 
     def get_urls(self):
         """
diff --git a/rest_framework/tests/test_routers.py b/rest_framework/tests/test_routers.py
index e723f7d45..8b5cd4fbe 100644
--- a/rest_framework/tests/test_routers.py
+++ b/rest_framework/tests/test_routers.py
@@ -121,6 +121,27 @@ class TestCustomLookupFields(TestCase):
         )
 
 
+class TestLookupValueRegex(TestCase):
+    """
+    Ensure the router honors lookup_value_regex when applied
+    to the viewset.
+    """
+    def setUp(self):
+        class NoteViewSet(viewsets.ModelViewSet):
+            queryset = RouterTestModel.objects.all()
+            lookup_field = 'uuid'
+            lookup_value_regex = '[0-9a-f]{32}'
+
+        self.router = SimpleRouter()
+        self.router.register(r'notes', NoteViewSet)
+        self.urls = self.router.urls
+
+    def test_urls_limited_by_lookup_value_regex(self):
+        expected = ['^notes/$', '^notes/(?P<uuid>[0-9a-f]{32})/$']
+        for idx in range(len(expected)):
+            self.assertEqual(expected[idx], self.urls[idx].regex.pattern)
+
+
 class TestTrailingSlashIncluded(TestCase):
     def setUp(self):
         class NoteViewSet(viewsets.ModelViewSet):