We focus on the problem of computing an -Nash equilibrium of a bimatrix game, when is an absolute constant. We present a simple algorithm for computing a 3 -Nash equilibrium for any bimatrix game in 4 strongly polynomial time and we next show how to extend this algorithm so as to obtain a (potentially stronger) parameterized approximation. Namely, we present an algorithm that computes a 2+ë -Nash equilibrium, 4 where ë is the minimum, among all Nash equilibria, expected payoff of either player. The suggested algorithm runs in time polynomial in the number of strategies available to the players.