diff --git a/doc/TODO b/doc/TODO
index be3a93c70..f829ac6cd 100644
--- a/doc/TODO
+++ b/doc/TODO
@@ -7,7 +7,6 @@ Before 0.1
     - Website
     - FAQ
 - Single-instance and multi-window
-- Tests for URL detection and fix corner cases
 - Maybe test under other platforms
 - Autosave feature (against segfaults/...)
 - Save tabs feature
diff --git a/qutebrowser/test/utils/test_url.py b/qutebrowser/test/utils/test_url.py
index c9c05e761..2dd858f78 100644
--- a/qutebrowser/test/utils/test_url.py
+++ b/qutebrowser/test/utils/test_url.py
@@ -126,6 +126,10 @@ class IsUrlTests(unittest.TestCase):
         'http://foobar',
         'localhost:8080',
         'qutebrowser.org',
+        '127.0.0.1',
+        '::1',
+        '2001:41d0:2:6c11::1',
+        '94.23.233.17',
     )
 
     NOT_URLS = (
@@ -133,6 +137,10 @@ class IsUrlTests(unittest.TestCase):
         'localhost test',
         'another . test',
         'foo',
+        'this is: not an URL',
+        '23.42',
+        '1337',
+        'deadbeef',
     )
 
     def test_urls(self, configmock):
diff --git a/qutebrowser/utils/urlutils.py b/qutebrowser/utils/urlutils.py
index fe431e224..21ffb6a30 100644
--- a/qutebrowser/utils/urlutils.py
+++ b/qutebrowser/utils/urlutils.py
@@ -21,6 +21,7 @@
 
 import re
 import os.path
+import ipaddress
 import urllib.parse
 
 from PyQt5.QtCore import QUrl
@@ -78,9 +79,18 @@ def _is_url_naive(urlstr):
         True if the URL really is a URL, False otherwise.
     """
     url = QUrl.fromUserInput(urlstr)
-    # We don't use url here because fromUserInput appends http://
-    # automatically.
-    if not url.isValid():
+    try:
+        ipaddress.ip_address(urlstr)
+    except ValueError:
+        pass
+    else:
+        # Valid IPv4/IPv6 address
+        return True
+    if re.search(r'^[0-9.]+$', urlstr):
+        # Qt treats things like "23.42" or "1337" as valid URLs which we don't
+        # want to. Note we already filtered *real* valid IPs above.
+        return False
+    elif not url.isValid():
         return False
     elif '.' in url.host():
         return True