diff --git a/wagtail/wagtailcore/blocks.py b/wagtail/wagtailcore/blocks.py
index c08c424bb..b476e6eb3 100644
--- a/wagtail/wagtailcore/blocks.py
+++ b/wagtail/wagtailcore/blocks.py
@@ -353,9 +353,6 @@ class FieldBlock(Block):
     def clean(self, value):
         return self.field.clean(value)
 
-    def get_searchable_content(self, value):
-        return [value]
-
 
 class CharBlock(FieldBlock):
     def __init__(self, required=True, help_text=None, max_length=None, min_length=None, **kwargs):
@@ -363,11 +360,16 @@ class CharBlock(FieldBlock):
         self.field = forms.CharField(required=required, help_text=help_text, max_length=max_length, min_length=min_length)
         super(CharBlock, self).__init__(**kwargs)
 
+    def get_searchable_content(self, value):
+        return [value]
+
+
 class URLBlock(FieldBlock):
     def __init__(self, required=True, help_text=None, max_length=None, min_length=None, **kwargs):
         self.field = forms.URLField(required=required, help_text=help_text, max_length=max_length, min_length=min_length)
         super(URLBlock, self).__init__(**kwargs)
 
+
 class RichTextBlock(FieldBlock):
     @cached_property
     def field(self):
@@ -377,6 +379,10 @@ class RichTextBlock(FieldBlock):
     def render_basic(self, value):
         return mark_safe('<div class="rich-text">' + expand_db_html(value) + '</div>')
 
+    def get_searchable_content(self, value):
+        return [value]
+
+
 class RawHTMLBlock(FieldBlock):
     def __init__(self, required=True, help_text=None, max_length=None, min_length=None, **kwargs):
         self.field = forms.CharField(
diff --git a/wagtail/wagtailcore/tests/test_blocks.py b/wagtail/wagtailcore/tests/test_blocks.py
index 06186633d..17bf1b81e 100644
--- a/wagtail/wagtailcore/tests/test_blocks.py
+++ b/wagtail/wagtailcore/tests/test_blocks.py
@@ -292,7 +292,7 @@ class TestStructBlock(unittest.TestCase):
             'link': 'http://www.wagtail.io',
         })
 
-        self.assertEqual(content, ["Wagtail site", "http://www.wagtail.io"])
+        self.assertEqual(content, ["Wagtail site"])
 
 
 class TestListBlock(unittest.TestCase):
@@ -447,7 +447,7 @@ class TestListBlock(unittest.TestCase):
             },
         ])
 
-        self.assertEqual(content, ["Wagtail", "http://www.wagtail.io", "Django", "http://www.djangoproject.com"])
+        self.assertEqual(content, ["Wagtail", "Django"])
 
 
 class TestStreamBlock(unittest.TestCase):