diff --git a/libvips/foreign/tiff2vips.c b/libvips/foreign/tiff2vips.c
index fe84780b..35046d81 100644
--- a/libvips/foreign/tiff2vips.c
+++ b/libvips/foreign/tiff2vips.c
@@ -1905,8 +1905,10 @@ vips__istiff_buffer( void *buf, size_t len )
 	char *str = (char *) buf; 
 
 	if( len >= 4 &&
-		((str[0] == 'M' && str[1] == 'M' && str[2] == '\0' && str[3] == '*') ||
-		 (str[0] == 'I' && str[1] == 'I' && str[2] == '*' && str[3] == '\0')) )
+		((str[0] == 'M' && str[1] == 'M' &&
+			str[2] == '\0' && (str[3] == '*' || str[3] == '+')) ||
+		(str[0] == 'I' && str[1] == 'I' &&
+			(str[2] == '*' || str[2] == '+') && str[3] == '\0')) )
 		return( TRUE );
 
 	return( FALSE );