This paper significantly improves the message complexity of perfect asynchronous secure computations among n players tolerating a computationally unbounded active adversary that corrupts up to t < n/4 players. The protocol presented in this paper communicates O(mn ³ lg ∣IF∣ + mn3 lg n) bits and broadcasts O(mn ²) bits, where m is the number of multiplication gates in the circuit. This is to be compared with the most efficient perfect secure asynchronous protocol known so far, namely the protocol of [5], which requires O(mn ⁴ lg ∣IF∣ + mn ⁴ lg n) bits of communication apart from O(mn ⁴ lg n) bits of broadcast.