diff --git a/doc/BUGS b/doc/BUGS
index d776bb0b8..89b2b3e5b 100644
--- a/doc/BUGS
+++ b/doc/BUGS
@@ -58,11 +58,6 @@ Crashes
 Qt warnings
 -----------
 
-- When following a hint:
-  QNetworkReplyImplPrivate::error: Internal problem, this method must only be called once.
-  Also when loading
-  https://web.archive.org/web/20140625053129/http://www.20min.ch/
-
 - Random error messages while browsing on imgur/reddit:
 
   WARNING: content-type missing in HTTP POST, defaulting to
diff --git a/qutebrowser/utils/log.py b/qutebrowser/utils/log.py
index b2199baea..0fd018248 100644
--- a/qutebrowser/utils/log.py
+++ b/qutebrowser/utils/log.py
@@ -234,9 +234,18 @@ def qt_message_handler(msg_type, context, msg):
     # Change levels of some well-known messages to debug so they don't get
     # shown to the user.
     # suppressed_msgs is a list of regexes matching the message texts to hide.
-    suppressed_msgs = ("libpng warning: iCCP: Not recognizing known sRGB "
-                       "profile that has been edited",
-                       "OpenType support missing for script [0-9]*")
+    suppressed_msgs = (
+        # PNGs in Qt with broken color profile
+        # https://bugreports.qt-project.org/browse/QTBUG-39788
+        "libpng warning: iCCP: Not recognizing known sRGB profile that has "
+        "been edited",
+        # Hopefully harmless warning
+        "OpenType support missing for script [0-9]*",
+        # Error if a QNetworkReply gets two different errors set. Harmless Qt
+        # bug on some pages.
+        # https://bugreports.qt-project.org/browse/QTBUG-30298
+        "QNetworkReplyImplPrivate::error: Internal problem, this method must "
+        "only be called once.")
     if any(re.match(pattern, msg.strip()) for pattern in suppressed_msgs):
         level = logging.DEBUG
     else: