diff --git a/pypdf/filters.py b/pypdf/filters.py
index e4aa6ea4c..461411d31 100644
--- a/pypdf/filters.py
+++ b/pypdf/filters.py
@@ -743,6 +743,7 @@ def bits2byte(data: bytes, size: Tuple[int, int], bits: int) -> bytes:
             return bytes(nbuff)
 
         extension = ".png"  # mime_type = "image/png"
+        image_format = "PNG"
         lookup: Any
         base: Any
         hival: Any
@@ -794,10 +795,14 @@ def bits2byte(data: bytes, size: Tuple[int, int], bits: int) -> bytes:
         elif not isinstance(color_space, NullObject) and color_space[0] == "/ICCBased":
             # see Table 66 - Additional Entries Specific to an ICC Profile
             # Stream Dictionary
-            mode = _get_imagemode(color_space, colors, mode)
-            extension = ".png"
-            img = Image.frombytes(mode, size, data)  # reloaded as mode may have change
-        image_format = "PNG"
+            mode2 = _get_imagemode(color_space, colors, mode)
+            if mode != mode2:
+                img = Image.frombytes(
+                    mode2, size, data
+                )  # reloaded as mode may have change
+        if mode == "CMYK":
+            extension = ".tif"
+            image_format = "TIFF"
         return img, image_format, extension
 
     def _handle_jpx(
@@ -907,7 +912,10 @@ def _handle_jpx(
 
     # CMYK image without decode requires reverting scale (cf p243,2§ last sentence)
     decode = x_object_obj.get(
-        IA.DECODE, ([1.0, 0.0] * 4) if img.mode == "CMYK" else None
+        IA.DECODE,
+        ([1.0, 0.0] * 4)
+        if img.mode == "CMYK" and lfilters in (FT.DCT_DECODE, FT.JPX_DECODE)
+        else None,
     )
     if (
         isinstance(color_space, ArrayObject)
diff --git a/tests/test_filters.py b/tests/test_filters.py
index 2eb8b58c0..7353a9bdf 100644
--- a/tests/test_filters.py
+++ b/tests/test_filters.py
@@ -388,6 +388,7 @@ def test_rgba():
 @pytest.mark.enable_socket()
 def test_cmyk():
     """Decode cmyk"""
+    # JPEG compression
     try:
         from Crypto.Cipher import AES  # noqa: F401
     except ImportError:
@@ -401,11 +402,30 @@ def test_cmyk():
         BytesIO(get_pdf_from_url(url_png, name=name_png))
     )  # not a pdf but it works
     data = reader.pages[1].images[0]
+    assert data.image.mode == "CMYK"
+    assert ".jpg" in data.name
     diff = ImageChops.difference(data.image, refimg)
     d = sqrt(
         sum([(a * a + b * b + c * c + d * d) for a, b, c, d in diff.getdata()])
     ) / (diff.size[0] * diff.size[1])
     assert d < 0.01
+    # deflate
+    url = "https://github.com/py-pdf/pypdf/files/12078533/cmyk2.pdf"
+    name = "cmyk_deflate.pdf"
+    reader = PdfReader(BytesIO(get_pdf_from_url(url, name=name)))
+    url_png = "https://github.com/py-pdf/pypdf/files/12078556/cmyk.tif.txt"
+    name_png = "cmyk_deflate.tif"
+    refimg = Image.open(
+        BytesIO(get_pdf_from_url(url_png, name=name_png))
+    )  # not a pdf but it works
+    data = reader.pages[0].images[0]
+    assert data.image.mode == "CMYK"
+    assert ".tif" in data.name
+    diff = ImageChops.difference(data.image, refimg)
+    d = sqrt(
+        sum([(a * a + b * b + c * c + d * d) for a, b, c, d in diff.getdata()])
+    ) / (diff.size[0] * diff.size[1])
+    assert d < 0.001  # lossless compression expected
 
 
 @pytest.mark.enable_socket()