diff --git a/Tests/test_file_gif.py b/Tests/test_file_gif.py
index fa5d54febf8..5bfb120f324 100644
--- a/Tests/test_file_gif.py
+++ b/Tests/test_file_gif.py
@@ -217,6 +217,27 @@ def test_optimize_if_palette_can_be_reduced_by_half():
             assert len(reloaded.palette.palette) // 3 == colors
 
 
+def test_full_palette_second_frame(tmp_path):
+    out = str(tmp_path / "temp.gif")
+    im = Image.new("P", (1, 256))
+
+    full_palette_im = Image.new("P", (1, 256))
+    for i in range(256):
+        full_palette_im.putpixel((0, i), i)
+    full_palette_im.palette = ImagePalette.ImagePalette(
+        "RGB", bytearray(i // 3 for i in range(768))
+    )
+    full_palette_im.palette.dirty = 1
+
+    im.save(out, save_all=True, append_images=[full_palette_im])
+
+    with Image.open(out) as reloaded:
+        reloaded.seek(1)
+
+        for i in range(256):
+            reloaded.getpixel((0, i)) == i
+
+
 def test_roundtrip(tmp_path):
     out = str(tmp_path / "temp.gif")
     im = hopper()
diff --git a/docs/handbook/image-file-formats.rst b/docs/handbook/image-file-formats.rst
index fe310df6443..5f64ec2343d 100644
--- a/docs/handbook/image-file-formats.rst
+++ b/docs/handbook/image-file-formats.rst
@@ -267,8 +267,9 @@ following options are available::
 
 **optimize**
     If present and true, attempt to compress the palette by
-    eliminating unused colors. This is only useful if the palette can
-    be compressed to the next smaller power of 2 elements.
+    eliminating unused colors (this is only useful if the palette can
+    be compressed to the next smaller power of 2 elements) and by marking
+    all pixels that are not new in the next frame as transparent.
 
 Note that if the image you are saving comes from an existing GIF, it may have
 the following properties in its :py:attr:`~PIL.Image.Image.info` dictionary.
diff --git a/src/PIL/GifImagePlugin.py b/src/PIL/GifImagePlugin.py
index bdea02005e7..fd0e8e6935c 100644
--- a/src/PIL/GifImagePlugin.py
+++ b/src/PIL/GifImagePlugin.py
@@ -30,7 +30,15 @@
 import subprocess
 from enum import IntEnum
 
-from . import Image, ImageChops, ImageFile, ImagePalette, ImageSequence
+from . import (
+    Image,
+    ImageChops,
+    ImageFile,
+    ImageMath,
+    ImageOps,
+    ImagePalette,
+    ImageSequence,
+)
 from ._binary import i16le as i16
 from ._binary import o8
 from ._binary import o16le as o16
@@ -562,13 +570,11 @@ def _write_single_frame(im, fp, palette):
 
 
 def _getbbox(base_im, im_frame):
-    if _get_palette_bytes(im_frame) == _get_palette_bytes(base_im):
-        delta = ImageChops.subtract_modulo(im_frame, base_im)
-    else:
-        delta = ImageChops.subtract_modulo(
-            im_frame.convert("RGBA"), base_im.convert("RGBA")
-        )
-    return delta.getbbox(alpha_only=False)
+    if _get_palette_bytes(im_frame) != _get_palette_bytes(base_im):
+        im_frame = im_frame.convert("RGBA")
+        base_im = base_im.convert("RGBA")
+    delta = ImageChops.subtract_modulo(im_frame, base_im)
+    return delta, delta.getbbox(alpha_only=False)
 
 
 def _write_multiple_frames(im, fp, palette):
@@ -576,6 +582,7 @@ def _write_multiple_frames(im, fp, palette):
     disposal = im.encoderinfo.get("disposal", im.info.get("disposal"))
 
     im_frames = []
+    previous_im = None
     frame_count = 0
     background_im = None
     for imSequence in itertools.chain([im], im.encoderinfo.get("append_images", [])):
@@ -600,14 +607,16 @@ def _write_multiple_frames(im, fp, palette):
                 encoderinfo["disposal"] = disposal[frame_count]
             frame_count += 1
 
+            diff_frame = None
             if im_frames:
                 # delta frame
-                previous = im_frames[-1]
-                bbox = _getbbox(previous["im"], im_frame)
+                delta, bbox = _getbbox(previous_im, im_frame)
                 if not bbox:
                     # This frame is identical to the previous frame
                     if encoderinfo.get("duration"):
-                        previous["encoderinfo"]["duration"] += encoderinfo["duration"]
+                        im_frames[-1]["encoderinfo"]["duration"] += encoderinfo[
+                            "duration"
+                        ]
                     continue
                 if encoderinfo.get("disposal") == 2:
                     if background_im is None:
@@ -617,10 +626,44 @@ def _write_multiple_frames(im, fp, palette):
                         background = _get_background(im_frame, color)
                         background_im = Image.new("P", im_frame.size, background)
                         background_im.putpalette(im_frames[0]["im"].palette)
-                    bbox = _getbbox(background_im, im_frame)
+                    delta, bbox = _getbbox(background_im, im_frame)
+                if encoderinfo.get("optimize") and im_frame.mode != "1":
+                    if "transparency" not in encoderinfo:
+                        try:
+                            encoderinfo[
+                                "transparency"
+                            ] = im_frame.palette._new_color_index(im_frame)
+                        except ValueError:
+                            pass
+                    if "transparency" in encoderinfo:
+                        # When the delta is zero, fill the image with transparency
+                        diff_frame = im_frame.copy()
+                        fill = Image.new(
+                            "P", diff_frame.size, encoderinfo["transparency"]
+                        )
+                        if delta.mode == "RGBA":
+                            r, g, b, a = delta.split()
+                            mask = ImageMath.eval(
+                                "convert(max(max(max(r, g), b), a) * 255, '1')",
+                                r=r,
+                                g=g,
+                                b=b,
+                                a=a,
+                            )
+                        else:
+                            if delta.mode == "P":
+                                # Convert to L without considering palette
+                                delta_l = Image.new("L", delta.size)
+                                delta_l.putdata(delta.getdata())
+                                delta = delta_l
+                            mask = ImageMath.eval("convert(im * 255, '1')", im=delta)
+                        diff_frame.paste(fill, mask=ImageOps.invert(mask))
             else:
                 bbox = None
-            im_frames.append({"im": im_frame, "bbox": bbox, "encoderinfo": encoderinfo})
+            previous_im = im_frame
+            im_frames.append(
+                {"im": diff_frame or im_frame, "bbox": bbox, "encoderinfo": encoderinfo}
+            )
 
     if len(im_frames) > 1:
         for frame_data in im_frames:
@@ -802,7 +845,7 @@ def _get_optimize(im, info):
     :param info: encoderinfo
     :returns: list of indexes of palette entries in use, or None
     """
-    if im.mode in ("P", "L") and info and info.get("optimize", 0):
+    if im.mode in ("P", "L") and info and info.get("optimize"):
         # Potentially expensive operation.
 
         # The palette saves 3 bytes per color not used, but palette
diff --git a/src/PIL/ImagePalette.py b/src/PIL/ImagePalette.py
index cb4f1dba115..b7c8d03abcd 100644
--- a/src/PIL/ImagePalette.py
+++ b/src/PIL/ImagePalette.py
@@ -102,6 +102,30 @@ def tobytes(self):
     # Declare tostring as an alias for tobytes
     tostring = tobytes
 
+    def _new_color_index(self, image=None, e=None):
+        if not isinstance(self.palette, bytearray):
+            self._palette = bytearray(self.palette)
+        index = len(self.palette) // 3
+        special_colors = ()
+        if image:
+            special_colors = (
+                image.info.get("background"),
+                image.info.get("transparency"),
+            )
+            while index in special_colors:
+                index += 1
+        if index >= 256:
+            if image:
+                # Search for an unused index
+                for i, count in reversed(list(enumerate(image.histogram()))):
+                    if count == 0 and i not in special_colors:
+                        index = i
+                        break
+            if index >= 256:
+                msg = "cannot allocate more than 256 colors"
+                raise ValueError(msg) from e
+        return index
+
     def getcolor(self, color, image=None):
         """Given an rgb tuple, allocate palette entry.
 
@@ -124,27 +148,7 @@ def getcolor(self, color, image=None):
                 return self.colors[color]
             except KeyError as e:
                 # allocate new color slot
-                if not isinstance(self.palette, bytearray):
-                    self._palette = bytearray(self.palette)
-                index = len(self.palette) // 3
-                special_colors = ()
-                if image:
-                    special_colors = (
-                        image.info.get("background"),
-                        image.info.get("transparency"),
-                    )
-                while index in special_colors:
-                    index += 1
-                if index >= 256:
-                    if image:
-                        # Search for an unused index
-                        for i, count in reversed(list(enumerate(image.histogram()))):
-                            if count == 0 and i not in special_colors:
-                                index = i
-                                break
-                    if index >= 256:
-                        msg = "cannot allocate more than 256 colors"
-                        raise ValueError(msg) from e
+                index = self._new_color_index(image, e)
                 self.colors[color] = index
                 if index * 3 < len(self.palette):
                     self._palette = (