A Multi-Property-Preserving (MPP) hash function is a hash function that simultaneously preserves several security properties of the underlying compression function. The Merkle-Damgard with a Permutation (MDP) was shown to preserve unforgeability and pseudorandom oracle property. In this paper, we consider the most basic security properties of hash functions, namely collision resistance, second-preimage resistance, and preimage-resistance. We first show which of these properties are preserved by MDP in the dedicated-key setting. We also identify the properties preserved by four variants of MDP, and five other variants of Merkle-Damgard iterated hash functions. As a result, for the ten hash functions we analyze, we obtain their complete MPP characteristics.