In this paper, we propose a new player elimination technique and use it to design an efficient protocol for unconditionally secure multiparty computation tolerating generalized adversaries. Our protocol requires broadcast of O(nL ² log(∣F∣) bits (broadcast is simulated using Byzantine agreement) while the non-cryptographic linear secret sharing based protocols, without player elimination, invoke Byzantine agreement sub-protocol for O(mL ³ log(∣F∣) bits, where m is the number of multiplication gates in the arithmetic circuit, over the finite field F, that describes the functionality of the protocol and L is the size of the underlying linear secret sharing scheme tolerating the given adversary structure.