Many applications using cryptographic hash functions do not require collision resistance, but some kind of preimage resistance. That's also the reason why the widely used SHA-1 continues to be recommended in all applications except digital signatures after 2010. Recent work on preimage and second preimage attacks on reduced SHA-1 succeeding up to 48 out of 80 steps (with results barely below the 2n time complexity of brute-force search) suggest that there is plenty of security margin left. In this paper we show that the security margin is actually somewhat lower, when only second preimages are the goal. We do this by giving two