diff --git a/Tests/test_image_convert.py b/Tests/test_image_convert.py
index 1d6469819..1ffd012aa 100644
--- a/Tests/test_image_convert.py
+++ b/Tests/test_image_convert.py
@@ -135,6 +135,10 @@ def test_trns_l(tmp_path):
 
     f = str(tmp_path / "temp.png")
 
+    im_la = im.convert("LA")
+    assert "transparency" not in im_la.info
+    im_la.save(f)
+
     im_rgb = im.convert("RGB")
     assert im_rgb.info["transparency"] == (128, 128, 128)  # undone
     im_rgb.save(f)
diff --git a/src/PIL/Image.py b/src/PIL/Image.py
index c9265b5ab..352d77fe7 100644
--- a/src/PIL/Image.py
+++ b/src/PIL/Image.py
@@ -975,7 +975,9 @@ class Image:
         delete_trns = False
         # transparency handling
         if has_transparency:
-            if self.mode in ("1", "L", "I", "RGB") and mode == "RGBA":
+            if (self.mode in ("1", "L", "I") and mode in ("LA", "RGBA")) or (
+                self.mode == "RGB" and mode == "RGBA"
+            ):
                 # Use transparent conversion to promote from transparent
                 # color to an alpha channel.
                 new_im = self._new(
diff --git a/src/libImaging/Convert.c b/src/libImaging/Convert.c
index 0f200af6b..5a632ca42 100644
--- a/src/libImaging/Convert.c
+++ b/src/libImaging/Convert.c
@@ -1634,29 +1634,15 @@ ImagingConvertTransparent(Imaging imIn, const char *mode, int r, int g, int b) {
         return (Imaging)ImagingError_ModeError();
     }
 
-    if (!((strcmp(imIn->mode, "RGB") == 0 || strcmp(imIn->mode, "1") == 0 ||
-           strcmp(imIn->mode, "I") == 0 || strcmp(imIn->mode, "L") == 0) &&
-          strcmp(mode, "RGBA") == 0))
-#ifdef notdef
-    {
-        return (Imaging)ImagingError_ValueError("conversion not supported");
-    }
-#else
-    {
-        static char buf[100];
-        snprintf(
-            buf,
-            100,
-            "conversion from %.10s to %.10s not supported in convert_transparent",
-            imIn->mode,
-            mode);
-        return (Imaging)ImagingError_ValueError(buf);
-    }
-#endif
-
-    if (strcmp(imIn->mode, "RGB") == 0) {
+    if (strcmp(imIn->mode, "RGB") == 0 && strcmp(mode, "RGBA") == 0) {
         convert = rgb2rgba;
-    } else {
+    } else if ((strcmp(imIn->mode, "1") == 0 ||
+                strcmp(imIn->mode, "I") == 0 ||
+                strcmp(imIn->mode, "L") == 0
+               ) && (
+                strcmp(mode, "RGBA") == 0 ||
+                strcmp(mode, "LA") == 0
+               )) {
         if (strcmp(imIn->mode, "1") == 0) {
             convert = bit2rgb;
         } else if (strcmp(imIn->mode, "I") == 0) {
@@ -1665,6 +1651,15 @@ ImagingConvertTransparent(Imaging imIn, const char *mode, int r, int g, int b) {
             convert = l2rgb;
         }
         g = b = r;
+    } else {
+        static char buf[100];
+        snprintf(
+            buf,
+            100,
+            "conversion from %.10s to %.10s not supported in convert_transparent",
+            imIn->mode,
+            mode);
+        return (Imaging)ImagingError_ValueError(buf);
     }
 
     imOut = ImagingNew2Dirty(mode, imOut, imIn);