We provide a concrete security treatment of several "provably secure" hash functions. Interpreting arguments behind MQ-HASH, FSB, SWIFFTX and VSH we identify similar lines of reasoning. We aim to formulate the main security claims in a language closer to that of attacks. We evaluate designers' claims of provable security and quantify them more precisely, deriving "second order" bounds on bounds. While the authors of FSB, MQ-HASH and SWIFFT(X) prove existence of non-trivial lower bounds on security, we show that the quantification of the bounds limits the practical significance of the proofs.