diff --git a/Tests/test_image_putpalette.py b/Tests/test_image_putpalette.py
index 3b29769a7a4..665e08a7e0e 100644
--- a/Tests/test_image_putpalette.py
+++ b/Tests/test_image_putpalette.py
@@ -32,6 +32,14 @@ def palette(mode):
     with pytest.raises(ValueError):
         palette("YCbCr")
 
+    with Image.open("Tests/images/hopper_gray.jpg") as im:
+        assert im.mode == "L"
+        im.putpalette(list(range(256)) * 3)
+
+    with Image.open("Tests/images/la.tga") as im:
+        assert im.mode == "LA"
+        im.putpalette(list(range(256)) * 3)
+
 
 def test_imagepalette():
     im = hopper("P")
diff --git a/src/libImaging/Unpack.c b/src/libImaging/Unpack.c
index a0fa22c7d3e..206403ba6e0 100644
--- a/src/libImaging/Unpack.c
+++ b/src/libImaging/Unpack.c
@@ -1552,10 +1552,12 @@ static struct {
     {"P", "P;4L", 4, unpackP4L},
     {"P", "P", 8, copy1},
     {"P", "P;R", 8, unpackLR},
+    {"P", "L", 8, copy1},
 
     /* palette w. alpha */
     {"PA", "PA", 16, unpackLA},
     {"PA", "PA;L", 16, unpackLAL},
+    {"PA", "LA", 16, unpackLA},
 
     /* true colour */
     {"RGB", "RGB", 24, ImagingUnpackRGB},