diff --git a/Lib/fontTools/subset/__init__.py b/Lib/fontTools/subset/__init__.py
index 56d9c0ef5..b9d358564 100644
--- a/Lib/fontTools/subset/__init__.py
+++ b/Lib/fontTools/subset/__init__.py
@@ -636,10 +636,16 @@ def prune_post_subset(self, font, options):
 			self.Value.prune_hints()
 		self.ValueFormat = self.Value.getEffectiveFormat()
 	elif self.Format == 2:
-		if not options.hinting:
-			for v in self.Value:
-				v.prune_hints()
-		self.ValueFormat = reduce(int.__or__, [v.getEffectiveFormat() for v in self.Value], 0)
+		if None in self.Value:
+			assert self.ValueFormat == 0
+			assert all(v is None for v in self.Value)
+		else:
+			if not options.hinting:
+				for v in self.Value:
+					v.prune_hints()
+			self.ValueFormat = reduce(
+				int.__or__, [v.getEffectiveFormat() for v in self.Value], 0
+			)
 
 	# Downgrade to Format 1 if all ValueRecords are the same
 	if self.Format == 2 and all(v == self.Value[0] for v in self.Value):
diff --git a/Tests/subset/subset_test.py b/Tests/subset/subset_test.py
index facafb2a7..2c51a5a9e 100644
--- a/Tests/subset/subset_test.py
+++ b/Tests/subset/subset_test.py
@@ -953,7 +953,8 @@ def test_subset_feature_variations_drop_all(featureVarsTestFont):
 # https://github.com/fonttools/fonttools/issues/1881#issuecomment-619415044
 
 
-def test_subset_single_pos_format():
+@pytest.fixture
+def singlepos2_font():
     fb = FontBuilder(unitsPerEm=1000)
     fb.setupGlyphOrder([".notdef", "a", "b", "c"])
     fb.setupCharacterMap({ord("a"): "a", ord("b"): "b", ord("c"): "c"})
@@ -971,8 +972,11 @@ def test_subset_single_pos_format():
     fb.save(buf)
     buf.seek(0)
 
-    font = TTFont(buf)
+    return TTFont(buf)
 
+
+def test_subset_single_pos_format(singlepos2_font):
+    font = singlepos2_font
     # The input font has a SinglePos Format 2 subtable where each glyph has
     # different ValueRecords
     assert getXML(font["GPOS"].table.LookupList.Lookup[0].toXML, font) == [
@@ -1018,6 +1022,46 @@ def test_subset_single_pos_format():
         '</Lookup>',
     ]
 
+def test_subset_single_pos_format2_all_None(singlepos2_font):
+    # https://github.com/fonttools/fonttools/issues/2602
+    font = singlepos2_font
+    gpos = font["GPOS"].table
+    subtable = gpos.LookupList.Lookup[0].SubTable[0]
+    assert subtable.Format == 2
+    # Hack a SinglePosFormat2 with ValueFormat = 0; our own buildSinglePos
+    # never makes these as a SinglePosFormat1 is more compact, but they can
+    # be found in the wild.
+    subtable.Value = [None] * subtable.ValueCount
+    subtable.ValueFormat = 0
+
+    assert getXML(subtable.toXML, font) == [
+        '<SinglePos Format="2">',
+        '  <Coverage>',
+        '    <Glyph value="a"/>',
+        '    <Glyph value="b"/>',
+        '    <Glyph value="c"/>',
+        '  </Coverage>',
+        '  <ValueFormat value="0"/>',
+        '  <!-- ValueCount=3 -->',
+        '</SinglePos>',
+    ]
+
+    options = subset.Options()
+    subsetter = subset.Subsetter(options)
+    subsetter.populate(unicodes=[ord("a"), ord("c")])
+    subsetter.subset(font)
+
+    # Check it was downgraded to Format1 after subsetting
+    assert getXML(font["GPOS"].table.LookupList.Lookup[0].SubTable[0].toXML, font) == [
+        '<SinglePos Format="1">',
+        '  <Coverage>',
+        '    <Glyph value="a"/>',
+        '    <Glyph value="c"/>',
+        '  </Coverage>',
+        '  <ValueFormat value="0"/>',
+        '</SinglePos>',
+    ]
+
 
 @pytest.fixture
 def ttf_path(tmp_path):