diff --git a/Lib/fontTools/ttLib/ttFont.py b/Lib/fontTools/ttLib/ttFont.py
index dbfcb6e89..e6fe9a673 100644
--- a/Lib/fontTools/ttLib/ttFont.py
+++ b/Lib/fontTools/ttLib/ttFont.py
@@ -487,6 +487,13 @@ class TTFont(object):
 				# in combination with the Adobe Glyph List (AGL).
 				#
 				self._getGlyphNamesFromCmap()
+			elif len(glyphOrder) < self['maxp'].numGlyphs:
+				#
+				# Not enough names found in the 'post' table.
+				# Can happen when 'post' format 1 is improperly used on a font that
+				# has more than 258 glyphs (the lenght of 'standardGlyphOrder').
+				#
+				self._getGlyphNamesFromCmap()
 			else:
 				self.glyphOrder = glyphOrder
 		else:
diff --git a/Tests/ttLib/data/bogus_post_format_1.ttf b/Tests/ttLib/data/bogus_post_format_1.ttf
new file mode 100644
index 000000000..62b80213c
Binary files /dev/null and b/Tests/ttLib/data/bogus_post_format_1.ttf differ
diff --git a/Tests/ttLib/ttFont_test.py b/Tests/ttLib/ttFont_test.py
index ad0810612..3cf7075e3 100644
--- a/Tests/ttLib/ttFont_test.py
+++ b/Tests/ttLib/ttFont_test.py
@@ -4,6 +4,7 @@ import re
 import random
 from fontTools.feaLib.builder import addOpenTypeFeaturesFromString
 from fontTools.ttLib import TTFont, TTLibError, newTable, registerCustomTableClass, unregisterCustomTableClass
+from fontTools.ttLib.standardGlyphOrder import standardGlyphOrder
 from fontTools.ttLib.tables.DefaultTable import DefaultTable
 from fontTools.ttLib.tables._c_m_a_p import CmapSubtable
 import pytest
@@ -143,6 +144,13 @@ def test_setGlyphOrder_also_updates_glyf_glyphOrder():
     assert font["glyf"].glyphOrder == new_order
 
 
+def test_getGlyphOrder_not_true_post_format_1():
+    # https://github.com/fonttools/fonttools/issues/2736
+    font = TTFont(os.path.join(DATA_DIR, "bogus_post_format_1.ttf"))
+    hmtx = font["hmtx"]
+    assert len(hmtx.metrics) > len(standardGlyphOrder)
+
+
 @pytest.mark.parametrize("lazy", [None, True, False])
 def test_ensureDecompiled(lazy):
     # test that no matter the lazy value, ensureDecompiled decompiles all tables