diff --git a/libvips/foreign/heifload.c b/libvips/foreign/heifload.c
index 646f2a93..a219ee5b 100644
--- a/libvips/foreign/heifload.c
+++ b/libvips/foreign/heifload.c
@@ -260,9 +260,15 @@ static const char *heif_magic[] = {
 static int
 vips_foreign_load_heif_is_a( const char *buf, int len )
 {
+	static unsigned char iso[4] = { 0, 0, 0, 24 };
+	static unsigned char three_gp[4] = { 0, 0, 0, 32 };
+
 	if( len >= 12 ) {
 		int i;
 
+		if ( memcmp( buf, iso, 4 ) != 0 && memcmp( buf, three_gp, 4 ) != 0 )
+			return ( 0 );
+
 		for( i = 0; i < VIPS_NUMBER( heif_magic ); i++ )
 			if( strncmp( buf + 4, heif_magic[i], 8 ) == 0 )
 				return( 1 );