First we revisit three - BGLS, MBGLS and GZZ verifiably encrypted signature schemes [2, 3, 6]. We find that they are all not strong unforgeable.We remark that the notion of existential unforgeable is not sufficient for fair exchange protocols in most circumstances.So we propose three new - NBGLS, MBGLS and NGZZ verifiably encrypted signature schemes which are strong unforgeable. Also we reconsider other two - ZSS and CA verifiably encrypted signature schemes [4, 8], we find that they both cannot resist replacing public key attack. So we strongly suggest that strong unforgeable for verifiably encrypted signature maybe a better notion than existential unforgeable and checking adjudicator knowing its private key is a necessary step for secure verifiably encrypted signature scheme.