diff --git a/docs/reference/pages/queryset_reference.rst b/docs/reference/pages/queryset_reference.rst
index 8fba3738f7..5ec52acd6a 100644
--- a/docs/reference/pages/queryset_reference.rst
+++ b/docs/reference/pages/queryset_reference.rst
@@ -202,6 +202,24 @@ Reference
 
     .. automethod:: not_type
 
+    .. automethod:: exact_type
+
+        Example:
+
+        .. code-block:: python
+
+            # Find all pages that are of the exact type EventPage
+            event_pages = Page.objects.exact_type(EventPage)
+
+    .. automethod:: not_exact_type
+
+        Example:
+
+        .. code-block:: python
+
+            # Find all pages that are not of the exact type EventPage (but may be a subclass)
+            non_event_pages = Page.objects.not_exact_type(EventPage)
+
     .. automethod:: unpublish
 
         Example:
diff --git a/wagtail/wagtailcore/management/commands/replace_text.py b/wagtail/wagtailcore/management/commands/replace_text.py
index 8893f1aa1c..95837de649 100644
--- a/wagtail/wagtailcore/management/commands/replace_text.py
+++ b/wagtail/wagtailcore/management/commands/replace_text.py
@@ -32,7 +32,10 @@ class Command(BaseCommand):
 
             child_relation_names = [rel.get_accessor_name() for rel in get_all_child_relations(page_class)]
 
-            for page in page_class.objects.all():
+            # Find all pages of this exact type; exclude subclasses, as they will
+            # appear in the get_page_models() list in their own right, and this
+            # ensures that replacement happens only once
+            for page in page_class.objects.exact_type(page_class):
                 replace_in_model(page, from_text, to_text)
                 for child_rel in child_relation_names:
                     for child in getattr(page, child_rel).all():
diff --git a/wagtail/wagtailcore/query.py b/wagtail/wagtailcore/query.py
index c3de7aa506..209ef8e3d3 100644
--- a/wagtail/wagtailcore/query.py
+++ b/wagtail/wagtailcore/query.py
@@ -191,6 +191,23 @@ class PageQuerySet(SearchableQuerySetMixin, TreeQuerySet):
         """
         return self.exclude(self.type_q(model))
 
+    def exact_type_q(self, klass):
+        return Q(content_type=ContentType.objects.get_for_model(klass))
+
+    def exact_type(self, model):
+        """
+        This filters the QuerySet to only contain pages that are an instance of the specified model
+        (matching the model exactly, not subclasses).
+        """
+        return self.filter(self.exact_type_q(model))
+
+    def not_exact_type(self, model):
+        """
+        This filters the QuerySet to not contain any pages which are an instance of the specified model
+        (matching the model exactly, not subclasses).
+        """
+        return self.exclude(self.exact_type_q(model))
+
     def public_q(self):
         from wagtail.wagtailcore.models import PageViewRestriction
 
diff --git a/wagtail/wagtailcore/tests/test_page_queryset.py b/wagtail/wagtailcore/tests/test_page_queryset.py
index 473f284dd2..91901e9f76 100644
--- a/wagtail/wagtailcore/tests/test_page_queryset.py
+++ b/wagtail/wagtailcore/tests/test_page_queryset.py
@@ -294,6 +294,11 @@ class TestPageQuerySet(TestCase):
         event = Page.objects.get(url_path='/home/events/someone-elses-event/')
         self.assertTrue(pages.filter(id=event.id).exists())
 
+        # Check that "Saint Patrick" (an instance of SingleEventPage, a subclass of EventPage)
+        # is in the results
+        event = Page.objects.get(url_path='/home/events/saint-patrick/')
+        self.assertTrue(pages.filter(id=event.id).exists())
+
     def test_type_includes_subclasses(self):
         from wagtail.wagtailforms.models import AbstractEmailForm
         pages = Page.objects.type(AbstractEmailForm)
@@ -317,6 +322,38 @@ class TestPageQuerySet(TestCase):
         homepage = Page.objects.get(url_path='/home/')
         self.assertTrue(pages.filter(id=homepage.id).exists())
 
+    def test_exact_type(self):
+        pages = Page.objects.exact_type(EventPage)
+
+        # Check that all objects are EventPages (and not a subclass)
+        for page in pages:
+            self.assertEqual(type(page.specific), EventPage)
+
+        # Check that "someone elses event" is in the results
+        event = Page.objects.get(url_path='/home/events/someone-elses-event/')
+        self.assertTrue(pages.filter(id=event.id).exists())
+
+        # Check that "Saint Patrick" (an instance of SingleEventPage, a subclass of EventPage)
+        # is NOT in the results
+        event = Page.objects.get(url_path='/home/events/saint-patrick/')
+        self.assertFalse(pages.filter(id=event.id).exists())
+
+    def test_not_exact_type(self):
+        pages = Page.objects.not_exact_type(EventPage)
+
+        # Check that no objects are EventPages
+        for page in pages:
+            self.assertNotEqual(type(page.specific), EventPage)
+
+        # Check that the homepage is in the results
+        homepage = Page.objects.get(url_path='/home/')
+        self.assertTrue(pages.filter(id=homepage.id).exists())
+
+        # Check that "Saint Patrick" (an instance of SingleEventPage, a subclass of EventPage)
+        # is in the results
+        event = Page.objects.get(url_path='/home/events/saint-patrick/')
+        self.assertTrue(pages.filter(id=event.id).exists())
+
     def test_public(self):
         events_index = Page.objects.get(url_path='/home/events/')
         event = Page.objects.get(url_path='/home/events/christmas/')