diff --git a/Tests/test_file_tiff.py b/Tests/test_file_tiff.py
index cf169a3ec5a..3d6f946728c 100644
--- a/Tests/test_file_tiff.py
+++ b/Tests/test_file_tiff.py
@@ -155,6 +155,45 @@ def test_bigtiff_save_big_endian_ifd(self, tmp_path: Path) -> None:
         ifd.load(BytesIO(data))
         assert ifd.tagtype[32768] == TiffTags.LONG8
 
+    def test_bigtiff_save_two_strips(self, tmp_path: Path) -> None:
+        outfile = tmp_path / "temp.tif"
+        im = hopper("L")
+
+        # Two LONG strip offsets fit within a BigTIFF entry
+        im.save(outfile, big_tiff=True, tiffinfo={TiffImagePlugin.ROWSPERSTRIP: 64})
+
+        with Image.open(outfile) as reloaded:
+            assert isinstance(reloaded, TiffImagePlugin.TiffImageFile)
+            assert len(reloaded.tag_v2[TiffImagePlugin.STRIPOFFSETS]) == 2
+            assert_image_equal(reloaded, im)
+
+    def test_bigtiff_save_big_endian_strip_offset(self, tmp_path: Path) -> None:
+        outfile = tmp_path / "temp.tif"
+        # I;16B is saved as big-endian
+        im = hopper("I;16B")
+
+        # The single LONG strip offset fits within a BigTIFF entry
+        im.save(outfile, big_tiff=True)
+
+        with Image.open(outfile) as reloaded:
+            assert isinstance(reloaded, TiffImagePlugin.TiffImageFile)
+            assert reloaded.tag_v2.prefix == b"MM"
+            assert reloaded.tag_v2._bigtiff is True
+            assert (
+                reloaded.tag_v2.tagtype[TiffImagePlugin.STRIPOFFSETS] == TiffTags.LONG
+            )
+            assert len(reloaded.tag_v2[TiffImagePlugin.STRIPOFFSETS]) == 1
+            assert_image_equal(reloaded, im)
+
+            # Check that the strip offset is upgraded to LONG8
+            # when it is too large for a LONG
+            data = reloaded.tag_v2.tobytes(2**32)
+
+        ifd = TiffImagePlugin.ImageFileDirectory_v2(b"MM\x00\x2b" + b"\x00" * 12)
+        ifd.load(BytesIO(data))
+        assert ifd.tagtype[TiffImagePlugin.STRIPOFFSETS] == TiffTags.LONG8
+        assert ifd[TiffImagePlugin.STRIPOFFSETS][0] > 2**32
+
     def test_seek_too_large(self) -> None:
         with pytest.raises(ValueError, match="Unable to seek to frame"):
             Image.open("Tests/images/seek_too_large.tif")
diff --git a/src/PIL/TiffImagePlugin.py b/src/PIL/TiffImagePlugin.py
index 6b26b4fb0fb..be8dd435e7f 100644
--- a/src/PIL/TiffImagePlugin.py
+++ b/src/PIL/TiffImagePlugin.py
@@ -1054,12 +1054,25 @@ def tobytes(self, offset: int = 0) -> bytes:
         # update strip offset data to point beyond auxiliary data
         if stripoffsets is not None:
             tag, typ, count, value, data = entries[stripoffsets]
+            size, handler = self._load_dispatch[typ]
+            values = [
+                val + offset for val in handler(self, data or value, self.legacy_api)
+            ]
             if data:
-                size, handler = self._load_dispatch[typ]
-                values = [val + offset for val in handler(self, data, self.legacy_api)]
                 data = self._write_dispatch[typ](self, *values)
             else:
-                value = self._pack(fmt, self._unpack(fmt, value)[0] + offset)
+                # The offsets fit within the entry
+                # May be one offset, or two LONG offsets in BigTIFF
+                if (
+                    self._bigtiff
+                    and typ == TiffTags.LONG
+                    and count == 1
+                    and values[0] >= 2**32
+                ):
+                    # If a single offset is too large for a LONG,
+                    # in BigTIFF there is room to change the entry to LONG8
+                    typ = TiffTags.LONG8
+                value = self._write_dispatch[typ](self, *values).ljust(fmt_size, b"\0")
             entries[stripoffsets] = tag, typ, count, value, data
 
         # pass 2: write entries to file