diff --git a/Lib/fontTools/misc/testTools.py b/Lib/fontTools/misc/testTools.py
index 0978ed040..dcd82cb56 100644
--- a/Lib/fontTools/misc/testTools.py
+++ b/Lib/fontTools/misc/testTools.py
@@ -62,6 +62,8 @@ class FakeFont:
             return self.glyphOrder_[glyphID]
         else:
             return "glyph%.5d" % glyphID
+    def getGlyphNameMany(self, lst):
+        return [self.getGlyphName(gid) for gid in lst]
 
     def getGlyphOrder(self):
         return self.glyphOrder_
diff --git a/Lib/fontTools/ttLib/tables/_c_m_a_p.py b/Lib/fontTools/ttLib/tables/_c_m_a_p.py
index 19b5998d6..d129391ee 100644
--- a/Lib/fontTools/ttLib/tables/_c_m_a_p.py
+++ b/Lib/fontTools/ttLib/tables/_c_m_a_p.py
@@ -14,15 +14,12 @@ log = logging.getLogger(__name__)
 
 def _make_map(font, chars, gids):
 	assert len(chars) == len(gids)
+	glyphNames = font.getGlyphNameMany(gids)
 	cmap = {}
 	glyphOrder = font.getGlyphOrder()
-	for char,gid in zip(chars,gids):
+	for char,gid,name in zip(chars,gids,glyphNames):
 		if gid == 0:
 			continue
-		try:
-			name = glyphOrder[gid]
-		except IndexError:
-			name = font.getGlyphName(gid)
 		cmap[char] = name
 	return cmap
 
diff --git a/Lib/fontTools/ttLib/tables/otConverters.py b/Lib/fontTools/ttLib/tables/otConverters.py
index 3733c079d..953df5778 100644
--- a/Lib/fontTools/ttLib/tables/otConverters.py
+++ b/Lib/fontTools/ttLib/tables/otConverters.py
@@ -347,14 +347,8 @@ class GlyphID(SimpleValue):
 	staticSize = 2
 	typecode = "H"
 	def readArray(self, reader, font, tableDict, count):
-		glyphOrder = font.getGlyphOrder()
 		gids = reader.readArray(self.typecode, self.staticSize, count)
-		try:
-			l = [glyphOrder[gid] for gid in gids]
-		except IndexError:
-			# Slower, but will not throw an IndexError on an invalid glyph id.
-			l = [font.getGlyphName(gid) for gid in gids]
-		return l
+		return font.getGlyphNameMany(gids)
 	def read(self, reader, font, tableDict):
 		return font.getGlyphName(reader.readValue(self.typecode, self.staticSize))
 	def writeArray(self, writer, font, tableDict, values):
@@ -1222,8 +1216,7 @@ class STXHeader(BaseConverter):
 	def _readLigatures(self, reader, font):
 		limit = len(reader.data)
 		numLigatureGlyphs = (limit - reader.pos) // 2
-		return [font.getGlyphName(g)
-		        for g in reader.readUShortArray(numLigatureGlyphs)]
+		return font.getGlyphNameMany (reader.readUShortArray(numLigatureGlyphs))
 
 	def _countPerGlyphLookups(self, table):
 		# Somewhat annoyingly, the morx table does not encode
diff --git a/Lib/fontTools/ttLib/tables/otTables.py b/Lib/fontTools/ttLib/tables/otTables.py
index c6ec31e4e..9dbbe8153 100644
--- a/Lib/fontTools/ttLib/tables/otTables.py
+++ b/Lib/fontTools/ttLib/tables/otTables.py
@@ -425,8 +425,7 @@ class InsertionMorphAction(AATAction):
 			return []
 		reader = actionReader.getSubReader(
 			actionReader.pos + index * 2)
-		return [font.getGlyphName(glyphID)
-		        for glyphID in reader.readUShortArray(count)]
+		return font.getGlyphNameMany(reader.readUShortArray(count))
 
 	def toXML(self, xmlWriter, font, attrs, name):
 		xmlWriter.begintag(name, **attrs)
@@ -538,8 +537,7 @@ class Coverage(FormatSwitchingBaseTable):
 				end = r.End
 				startID = font.getGlyphID(start)
 				endID = font.getGlyphID(end) + 1
-				for glyphID in range(startID, endID):
-					glyphs.append(font.getGlyphName(glyphID))
+				glyphs.extend(font.getGlyphNameMany(range(startID, endID)))
 		else:
 			self.glyphs = []
 			log.warning("Unknown Coverage format: %s", self.Format)
@@ -755,7 +753,7 @@ class SingleSubst(FormatSwitchingBaseTable):
 			delta = rawTable["DeltaGlyphID"]
 			inputGIDS =  [ font.getGlyphID(name) for name in input ]
 			outGIDS = [ (glyphID + delta) % 65536 for glyphID in inputGIDS ]
-			outNames = [ font.getGlyphName(glyphID) for glyphID in outGIDS ]
+			outNames = font.getGlyphNameMany(outGIDS)
 			for inp, out in zip(input, outNames):
 				mapping[inp] = out
 		elif self.Format == 2:
@@ -915,9 +913,10 @@ class ClassDef(FormatSwitchingBaseTable):
 			classList = rawTable["ClassValueArray"]
 			startID = font.getGlyphID(start)
 			endID = startID + len(classList)
-			for glyphID, cls in zip(range(startID, endID), classList):
+			glyphNames = font.getGlyphNameMany(range(startID, endID))
+			for glyphName, cls in zip(glyphNames, classList):
 				if cls:
-					classDefs[font.getGlyphName(glyphID)] = cls
+					classDefs[glyphName] = cls
 
 		elif self.Format == 2:
 			records = rawTable["ClassRangeRecord"]
@@ -927,9 +926,10 @@ class ClassDef(FormatSwitchingBaseTable):
 				cls = rec.Class
 				startID = font.getGlyphID(start)
 				endID = font.getGlyphID(end) + 1
-				for glyphID in range(startID, endID):
-					if cls:
-						classDefs[font.getGlyphName(glyphID)] = cls
+				glyphNames = font.getGlyphNameMany(range(startID, endID))
+				if cls:
+					for glyphName in glyphNames:
+						classDefs[glyphName] = cls
 		else:
 			log.warning("Unknown ClassDef format: %s", self.Format)
 		self.classDefs = classDefs
diff --git a/Lib/fontTools/ttLib/ttFont.py b/Lib/fontTools/ttLib/ttFont.py
index 1df67b58d..8ea0c5f81 100644
--- a/Lib/fontTools/ttLib/ttFont.py
+++ b/Lib/fontTools/ttLib/ttFont.py
@@ -533,6 +533,11 @@ class TTFont(object):
 			return self.getGlyphOrder()[glyphID]
 		except IndexError:
 			return "glyph%.5d" % glyphID
+	def getGlyphNameMany(self, lst):
+		glyphOrder = self.getGlyphOrder();
+		cnt = len(glyphOrder)
+		return [glyphOrder[gid] if gid < cnt else "glyph%.5d" % gid
+			for gid in lst]
 
 	def getGlyphID(self, glyphName):
 		if not hasattr(self, "_reverseGlyphOrderDict"):