diff --git a/src/PIL/Image.py b/src/PIL/Image.py
index 7fc8f496eeb..833473f789d 100644
--- a/src/PIL/Image.py
+++ b/src/PIL/Image.py
@@ -3268,8 +3268,14 @@ def _open_core(fp, filename, prefix, formats):
     im = _open_core(fp, filename, prefix, formats)
 
     if im is None and formats is ID:
+        checked_formats = formats.copy()
         if init():
-            im = _open_core(fp, filename, prefix, formats)
+            im = _open_core(
+                fp,
+                filename,
+                prefix,
+                tuple(format for format in formats if format not in checked_formats),
+            )
 
     if im:
         im._exclusive_fp = exclusive_fp