diff --git a/Lib/fontTools/varLib/varStore.py b/Lib/fontTools/varLib/varStore.py
index dcc36bb1e..f05f41f5d 100644
--- a/Lib/fontTools/varLib/varStore.py
+++ b/Lib/fontTools/varLib/varStore.py
@@ -470,7 +470,7 @@ class _EncodingDict(dict):
         return chars
 
 
-def VarStore_optimize(self, use_NO_VARIATION_INDEX=True):
+def VarStore_optimize(self, use_NO_VARIATION_INDEX=True, quantization=1):
     """Optimize storage. Returns mapping from old VarIdxes to new ones."""
 
     # Overview:
@@ -551,8 +551,16 @@ def VarStore_optimize(self, use_NO_VARIATION_INDEX=True):
 
         for minor, item in enumerate(data.Item):
             row = list(zeroes)
-            for regionIdx, v in zip(regionIndices, item):
-                row[regionIdx] += v
+
+            if quantization == 1:
+                for regionIdx, v in zip(regionIndices, item):
+                    row[regionIdx] += v
+            else:
+                for regionIdx, v in zip(regionIndices, item):
+                    row[regionIdx] += (
+                        round(v / quantization) * quantization
+                    )  # TODO https://github.com/fonttools/fonttools/pull/3126#discussion_r1205439785
+
             row = tuple(row)
 
             if use_NO_VARIATION_INDEX and not any(row):
@@ -684,6 +692,7 @@ def main(args=None):
     from fontTools.ttLib.tables.otBase import OTTableWriter
 
     parser = ArgumentParser(prog="varLib.varStore", description=main.__doc__)
+    parser.add_argument("--quantization", type=int, default=1)
     parser.add_argument("fontfile")
     parser.add_argument("outfile", nargs="?")
     options = parser.parse_args(args)
@@ -691,6 +700,7 @@ def main(args=None):
     # TODO: allow user to configure logging via command-line options
     configLogger(level="INFO")
 
+    quantization = options.quantization
     fontfile = options.fontfile
     outfile = options.outfile
 
@@ -703,7 +713,7 @@ def main(args=None):
     size = len(writer.getAllData())
     print("Before: %7d bytes" % size)
 
-    varidx_map = store.optimize()
+    varidx_map = store.optimize(quantization=quantization)
 
     writer = OTTableWriter()
     store.compile(writer, font)
diff --git a/Tests/varLib/varStore_test.py b/Tests/varLib/varStore_test.py
index 37447c051..70d1340f2 100644
--- a/Tests/varLib/varStore_test.py
+++ b/Tests/varLib/varStore_test.py
@@ -202,3 +202,57 @@ def test_optimize(numRegions, varData, expectedNumVarData, expectedBytes):
     data = writer.getAllData()
 
     assert len(data) == expectedBytes, xml
+
+
+@pytest.mark.parametrize(
+    "quantization, expectedBytes",
+    [
+        (1, 200),
+        (2, 180),
+        (3, 170),
+        (4, 175),
+        (8, 170),
+        (32, 152),
+        (64, 146),
+    ],
+)
+def test_quantize(quantization, expectedBytes):
+    varData = [
+        [0, 11, 12, 0, 20],
+        [0, 13, 12, 0, 20],
+        [0, 14, 12, 0, 20],
+        [0, 15, 12, 0, 20],
+        [0, 16, 12, 0, 20],
+        [10, 300, 0, 0, 20],
+        [10, 301, 0, 0, 20],
+        [10, 302, 0, 0, 20],
+        [10, 303, 0, 0, 20],
+        [10, 304, 0, 0, 20],
+    ]
+
+    numRegions = 5
+    locations = [{i: i / 16384.0} for i in range(numRegions)]
+    axisTags = sorted({k for loc in locations for k in loc})
+
+    model = VariationModel(locations)
+
+    builder = OnlineVarStoreBuilder(axisTags)
+    builder.setModel(model)
+
+    for data in varData:
+        builder.storeMasters(data)
+
+    varStore = builder.finish()
+    varStore.optimize(quantization=quantization)
+
+    dummyFont = TTFont()
+
+    writer = XMLWriter(StringIO())
+    varStore.toXML(writer, dummyFont)
+    xml = writer.file.getvalue()
+
+    writer = OTTableWriter()
+    varStore.compile(writer, dummyFont)
+    data = writer.getAllData()
+
+    assert len(data) == expectedBytes, xml