diff --git a/src/PIL/IcnsImagePlugin.py b/src/PIL/IcnsImagePlugin.py
index 069aff96b63..c22bfe0ed06 100644
--- a/src/PIL/IcnsImagePlugin.py
+++ b/src/PIL/IcnsImagePlugin.py
@@ -167,7 +167,7 @@ def __init__(self, fobj):
         self.dct = dct = {}
         self.fobj = fobj
         sig, filesize = nextheader(fobj)
-        if sig != MAGIC:
+        if not _accept(sig):
             raise SyntaxError("not an icns file")
         i = HEADERSIZE
         while i < filesize:
diff --git a/src/PIL/TiffImagePlugin.py b/src/PIL/TiffImagePlugin.py
index 35ff1c1bbf7..d8dc1741a3b 100644
--- a/src/PIL/TiffImagePlugin.py
+++ b/src/PIL/TiffImagePlugin.py
@@ -493,7 +493,7 @@ def __init__(self, ifh=b"II\052\0\0\0\0\0", prefix=None, group=None):
               endianness.
         :param prefix: Override the endianness of the file.
         """
-        if ifh[:4] not in PREFIXES:
+        if not _accept(ifh):
             raise SyntaxError(f"not a TIFF file (header {repr(ifh)} not valid)")
         self._prefix = prefix if prefix is not None else ifh[:2]
         if self._prefix == MM: