diff --git a/src/calibre/ebooks/oeb/polish/container.py b/src/calibre/ebooks/oeb/polish/container.py
index d9f5f5aac2..ece50b23c5 100644
--- a/src/calibre/ebooks/oeb/polish/container.py
+++ b/src/calibre/ebooks/oeb/polish/container.py
@@ -149,8 +149,14 @@ class ContainerBase(object):  # {{{
         ans = guess_type(name)
         if ans == 'text/html':
             ans = 'application/xhtml+xml'
-        if ans in {'application/x-font-truetype', 'application/vnd.ms-opentype'} and self.opf_version_parsed[:2] > (3, 0):
-            return 'application/font-sfnt'
+        if ans in {'application/x-font-truetype', 'application/vnd.ms-opentype'}:
+            opfversion = self.opf_version_parsed[:2]
+            if opfversion > (3, 0):
+                return 'application/font-sfnt'
+            if opfversion >= (3, 0):
+                # bloody epubcheck has recently decided it likes this mimetype
+                # for ttf files
+                return 'application/vnd.ms-opentype'
         return ans
 
     def decode(self, data, normalize_to_nfc=True):