diff --git a/src/PIL/TiffImagePlugin.py b/src/PIL/TiffImagePlugin.py
index d74af284fcd..58e9019283e 100644
--- a/src/PIL/TiffImagePlugin.py
+++ b/src/PIL/TiffImagePlugin.py
@@ -1553,8 +1553,13 @@ def _save(im, fp, filename):
         ifd[COLORMAP] = tuple(v * 256 for v in lut)
     # data orientation
     stride = len(bits) * ((im.size[0] * bits[0] + 7) // 8)
-    ifd[ROWSPERSTRIP] = im.size[1]
+    rows_per_strip = im.size[1]
     strip_byte_counts = stride * im.size[1]
+    # aim for 64 KB strips
+    while strip_byte_counts > 2 ** 16 and rows_per_strip > 1:
+        rows_per_strip = (rows_per_strip + 1) // 2
+        strip_byte_counts = stride * rows_per_strip
+    ifd[ROWSPERSTRIP] = rows_per_strip
     if strip_byte_counts >= 2 ** 16:
         ifd.tagtype[STRIPBYTECOUNTS] = TiffTags.LONG
     ifd[STRIPBYTECOUNTS] = strip_byte_counts