Accurate and efficient estimation of fading parameters are of considerable interest in the design of adaptive radios since they provide an indication of the communication link quality. In this letter, we develop a few simple estimators for the Nakagami-m, parameter by approximating the transcendental equations that arise in the computation of maximum-likelihood and generalized moment based estimators as linear of quadratic polynomials using quasinewton optimization method. Statistical properties and efficacy of the new estimators are validated via Monte Carlo simulations.