diff --git a/Tests/test_file_gif.py b/Tests/test_file_gif.py
index 3c2fab722..1bd772dc6 100644
--- a/Tests/test_file_gif.py
+++ b/Tests/test_file_gif.py
@@ -813,6 +813,29 @@ def test_zero_comment_subblocks():
         assert_image_equal_tofile(im, TEST_GIF)
 
 
+def test_write_comment(tmp_path):
+    out = str(tmp_path / "temp.gif")
+    with Image.open("Tests/images/multiple_comments.gif") as im:
+        im.save(out, save_all=True, comment="Test")
+        with Image.open(out) as reread:
+            # Comments written should appear only in first frame
+            assert reread.info["comment"] == b"Test"
+            for i, frame in enumerate(ImageSequence.Iterator(reread)):
+                assert (i == 0 and frame.info["comment"] == b"Test" or
+                        i != 0 and "comment" not in frame.info)
+
+
+def test_write_no_comment(tmp_path):
+    out = str(tmp_path / "temp.gif")
+    with Image.open("Tests/images/multiple_comments.gif") as im:
+        # Empty comment="" arg should suppress all comments
+        im.save(out, save_all=True, comment="")
+        with Image.open(out) as reread:
+            assert "comment" not in reread.info
+            for frame in ImageSequence.Iterator(reread):
+                assert "comment" not in frame.info
+
+
 def test_version(tmp_path):
     out = str(tmp_path / "temp.gif")
 
diff --git a/src/PIL/GifImagePlugin.py b/src/PIL/GifImagePlugin.py
index 9b34a3b0e..4d785d834 100644
--- a/src/PIL/GifImagePlugin.py
+++ b/src/PIL/GifImagePlugin.py
@@ -715,15 +715,6 @@ def _write_local_header(fp, im, offset, flags):
             + o8(0)
         )
 
-    if "comment" in im.encoderinfo and 1 <= len(im.encoderinfo["comment"]):
-        fp.write(b"!" + o8(254))  # extension intro
-        comment = im.encoderinfo["comment"]
-        if isinstance(comment, str):
-            comment = comment.encode()
-        for i in range(0, len(comment), 255):
-            subblock = comment[i : i + 255]
-            fp.write(o8(len(subblock)) + subblock)
-        fp.write(o8(0))
     if "loop" in im.encoderinfo:
         number_of_loops = im.encoderinfo["loop"]
         fp.write(
@@ -929,7 +920,7 @@ def _get_global_header(im, info):
     palette_bytes = _get_palette_bytes(im)
     color_table_size = _get_color_table_size(palette_bytes)
 
-    return [
+    header = [
         b"GIF"  # signature
         + version  # version
         + o16(im.size[0])  # canvas width
@@ -943,6 +934,18 @@ def _get_global_header(im, info):
         _get_header_palette(palette_bytes),
     ]
 
+    if "comment" in info and len(info["comment"]):
+        comment = info["comment"]
+        if isinstance(comment, str):
+            comment = comment.encode()
+        header.append(b"!" + o8(254))  # extension intro
+        for i in range(0, len(comment), 255):
+            subblock = comment[i : i + 255]
+            header.append(o8(len(subblock)) + subblock)
+        header.append(o8(0))
+
+    return header
+
 
 def _write_frame_data(fp, im_frame, offset, params):
     try: