diff --git a/src/PIL/TiffImagePlugin.py b/src/PIL/TiffImagePlugin.py
index 4b36666548d..f7c57c65113 100644
--- a/src/PIL/TiffImagePlugin.py
+++ b/src/PIL/TiffImagePlugin.py
@@ -1555,7 +1555,7 @@ def _save(im, fp, filename):
     stride = len(bits) * ((im.size[0] * bits[0] + 7) // 8)
     # aim for 64 KB strips when using libtiff writer
     if libtiff:
-        rows_per_strip = (2 ** 16 + stride - 1) // stride
+        rows_per_strip = min((2 ** 16 + stride - 1) // stride, im.size[1])
     else:
         rows_per_strip = im.size[1]
     strip_byte_counts = stride * rows_per_strip