In 2001, Bellare, Namprempre, Pointcheval and Semanko introduced the notion of "one-more" computational problems. Since their introduction, these problems have found numerous applications in cryptography. For instance, Bellare et al. showed how they lead to a proof of security for Chaum's RSA-based blind signature scheme in the random oracle model. In this paper, we provide separation results for the computational hierarchy of a large class of algebraic "one-more" computational problems (e.g. the one-more discrete logarithm problem, the one-more RSA problem and the one-more static Computational Diffie-Hellman problem in a bilinear setting). We also give some cryptographic implications of these results and, in particular, we prove that it is very unlikely, that one will ever be able to prove the unforgeability of Chaum's RSA-based blind signature scheme under the sole RSA assumption.