In this paper we present new attack techniques to analyze the structure of hash functions that are not based on the classical Merkle-Damgaard̊ construction. We extend the herding attack to concatenated hashes, and to certain hash functions that process each message block several times. Using this technique, we show a second preimage attack on the folklore “hash-twice” construction which process two concatenated copies of the message. We follow with showing how to apply the herding attack to tree hashes. Finally, we present a new type of attack — the trojan message attack, which allows for producing second preimages of unknown messages (from a small known space) when they are appended with a fixed suffix.