diff --git a/docs/api-guide/routers.md b/docs/api-guide/routers.md
index d2d65d951..91ef0b96e 100644
--- a/docs/api-guide/routers.md
+++ b/docs/api-guide/routers.md
@@ -167,17 +167,22 @@ 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.
 
-The router will match lookup values containing any characters except slashes and period characters.  For a more restrictive (or lenient) lookup pattern, set the `lookup_value_regex` attribute on the viewset.  For example, you can limit the lookup to valid UUIDs:
+By default the URLs created by `SimpleRouter` use regular expressions. This behavior can be modified by setting the `use_regex_path` argument to `False` when instantiating the router, in this case [path converters][path-converters-topic-reference] are used. For example:
+
+    router = SimpleRouter(use_regex_path=False)
+
+**Note**: `use_regex_path=False` only works with Django 2.x or above, since this feature was introduced in 2.0.0. See [release note][simplified-routing-release-note]
+
+
+The router will match lookup values containing any characters except slashes and period characters.  For a more restrictive (or lenient) lookup pattern, set the `lookup_value_regex` attribute on the viewset or `lookup_value_converter` if using path converters.  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}'
 
-By default, the URLs created by `SimpleRouter` use regular expressions. This behavior can be modified by setting the `use_regex_path` argument to `False` when instantiating the router, in this case [path converters][path-converters-topic-reference] are used. For example:
-
-    router = SimpleRouter(use_regex_path=False)
-
-**Note**: `use_regex_path=False` only works with Django 2.x or above, since this feature was introduced in 2.0.0. See [release note][simplified-routing-release-note]
+    class MyPathModelViewSet(mixins.RetrieveModelMixin, viewsets.GenericViewSet):
+        lookup_field = 'my_model_uuid'
+        lookup_value_converter = 'uuid'
 
 ## DefaultRouter
 
diff --git a/rest_framework/routers.py b/rest_framework/routers.py
index bcc280f13..5b9cc3674 100644
--- a/rest_framework/routers.py
+++ b/rest_framework/routers.py
@@ -125,13 +125,14 @@ class SimpleRouter(BaseRouter):
 
     def __init__(self, trailing_slash=True, use_regex_path=True):
         self.trailing_slash = '/' if trailing_slash else ''
+        self._use_regex = use_regex_path
         if use_regex_path:
-            self._base_regex = '(?P<{lookup_prefix}{lookup_url_kwarg}>{lookup_value})'
-            self._default_regex = '[^/.]+'
+            self._base_pattern = '(?P<{lookup_prefix}{lookup_url_kwarg}>{lookup_value})'
+            self._default_value_pattern = '[^/.]+'
             self._url_conf = re_path
         else:
-            self._base_regex = '<{lookup_value}:{lookup_prefix}{lookup_url_kwarg}>'
-            self._default_regex = 'path'
+            self._base_pattern = '<{lookup_value}:{lookup_prefix}{lookup_url_kwarg}>'
+            self._default_value_pattern = 'path'
             self._url_conf = path
             # remove regex characters from routes
             _routes = []
@@ -237,8 +238,14 @@ class SimpleRouter(BaseRouter):
         # consume `.json` style suffixes and should break at '/' boundaries.
         lookup_field = getattr(viewset, 'lookup_field', 'pk')
         lookup_url_kwarg = getattr(viewset, 'lookup_url_kwarg', None) or lookup_field
-        lookup_value = getattr(viewset, 'lookup_value_regex', self._default_regex)
-        return self._base_regex.format(
+        lookup_value = None
+        if not self._use_regex:
+            # try to get a more appropriate attribute when not using regex
+            lookup_value = getattr(viewset, 'lookup_value_converter', None)
+        if lookup_value is None:
+            # fallback to legacy
+            lookup_value = getattr(viewset, 'lookup_value_regex', self._default_value_pattern)
+        return self._base_pattern.format(
             lookup_prefix=lookup_prefix,
             lookup_url_kwarg=lookup_url_kwarg,
             lookup_value=lookup_value