diff --git a/src/calibre/ebooks/oeb/polish/subset.py b/src/calibre/ebooks/oeb/polish/subset.py
index a49bf7f78d..8dd90f9dd8 100644
--- a/src/calibre/ebooks/oeb/polish/subset.py
+++ b/src/calibre/ebooks/oeb/polish/subset.py
@@ -5,15 +5,16 @@ __license__   = 'GPL v3'
 __copyright__ = '2013, Kovid Goyal <kovid at kovidgoyal.net>'
 __docformat__ = 'restructuredtext en'
 
-import os, sys
+import os
+import sys
+from io import BytesIO
 
-from calibre import prints, as_unicode
-from calibre.ebooks.oeb.base import OEB_STYLES, OEB_DOCS, XPath, css_text
-from calibre.ebooks.oeb.polish.utils import guess_type, OEB_FONTS
-from calibre.utils.fonts.sfnt.subset import subset
-from calibre.utils.fonts.sfnt.errors import UnsupportedFont
+from calibre import as_unicode, prints
+from calibre.ebooks.oeb.base import OEB_DOCS, OEB_STYLES, XPath, css_text
+from calibre.ebooks.oeb.polish.utils import OEB_FONTS
+from calibre.utils.fonts.subset import subset
 from calibre.utils.fonts.utils import get_font_names
-from polyglot.builtins import iteritems, itervalues
+from polyglot.builtins import iteritems
 
 
 def remove_font_face_rules(container, sheet, remove_names, base):
@@ -33,9 +34,8 @@ def remove_font_face_rules(container, sheet, remove_names, base):
 
 
 def iter_subsettable_fonts(container):
-    woff_font_types = guess_type('a.woff'), guess_type('a.woff2')
     for name, mt in iteritems(container.mime_map):
-        if (mt in OEB_FONTS or name.rpartition('.')[-1].lower() in {'otf', 'ttf'}) and mt not in woff_font_types:
+        if (mt in OEB_FONTS or name.rpartition('.')[-1].lower() in {'otf', 'ttf'}):
             yield name, mt
 
 
@@ -63,20 +63,22 @@ def subset_all_fonts(container, font_stats, report):
                 continue
             warnings = []
             report('Subsetting font: %s'%(font_name or name))
+            font_type = os.path.splitext(name)[1][1:].lower()
+            output = BytesIO()
             try:
-                nraw, old_sizes, new_sizes = subset(raw, chars,
-                                                warnings=warnings)
-            except UnsupportedFont as e:
+                warnings = subset(BytesIO(raw), output, font_type, chars)
+            except Exception as e:
                 report(
                     'Unsupported font: %s, ignoring. Error: %s'%(
                         name, as_unicode(e)))
                 continue
+            nraw = output.getvalue()
             total_old += font_size
 
             for w in warnings:
                 report(w)
-            olen = sum(itervalues(old_sizes))
-            nlen = sum(itervalues(new_sizes))
+            olen = len(raw)
+            nlen = len(nraw)
             total_new += len(nraw)
             if nlen == olen:
                 report(_('The font %s was already subset')%font_name)
diff --git a/src/calibre/ebooks/oeb/transforms/subset.py b/src/calibre/ebooks/oeb/transforms/subset.py
index a11f295a7f..604d8083f7 100644
--- a/src/calibre/ebooks/oeb/transforms/subset.py
+++ b/src/calibre/ebooks/oeb/transforms/subset.py
@@ -5,11 +5,13 @@ __license__   = 'GPL v3'
 __copyright__ = '2012, Kovid Goyal <kovid at kovidgoyal.net>'
 __docformat__ = 'restructuredtext en'
 
+import os
 from collections import defaultdict
+from io import BytesIO
 
-from calibre.ebooks.oeb.base import urlnormalize, css_text
-from calibre.utils.fonts.sfnt.subset import subset, NoGlyphs, UnsupportedFont
-from polyglot.builtins import iteritems, itervalues
+from calibre.ebooks.oeb.base import css_text, urlnormalize
+from calibre.utils.fonts.subset import subset
+from polyglot.builtins import iteritems
 from tinycss.fonts3 import parse_font_family
 
 
@@ -150,27 +152,25 @@ class SubsetFonts:
             else:
                 fonts[item.href] = font
 
-        for font in itervalues(fonts):
+        for font in fonts.values():
             if not font['chars']:
                 self.log('The font %s is unused. Removing it.'%font['src'])
                 remove(font)
                 continue
+            old_raw = font['item'].data
+            output = BytesIO()
+            font_type = os.path.splitext(font['item'].href)[1][1:].lower()
             try:
-                raw, old_stats, new_stats = subset(font['item'].data, font['chars'])
-            except NoGlyphs:
-                self.log('The font %s has no used glyphs. Removing it.'%font['src'])
-                remove(font)
-                continue
-            except UnsupportedFont as e:
-                self.log.warn('The font %s is unsupported for subsetting. %s'%(
-                    font['src'], e))
+                subset(BytesIO(old_raw), output, font_type, font['chars'])
+            except Exception as e:
+                self.log.warn('The font %s is unsupported for subsetting. %s'%(font['src'], e))
                 sz = len(font['item'].data)
                 totals[0] += sz
                 totals[1] += sz
             else:
-                font['item'].data = raw
-                nlen = sum(itervalues(new_stats))
-                olen = sum(itervalues(old_stats))
+                font['item'].data = output.getvalue()
+                nlen = len(font['item'].data)
+                olen = len(old_raw)
                 self.log('Decreased the font %s to %.1f%% of its original size'%
                         (font['src'], nlen/olen *100))
                 totals[0] += nlen