Recent advances in the description of environmental and geophysical extreme events allow incorporating smooth time variations for the parameters of the GEV distribution using harmonic functions, long-term trends and covariates (North Atlantic Oscillation, El Niño, etc.). Most of the proposed models rely on the maximum likelihood estimation method for a given parameterization. However, finding the best parameter selection for each case is not an easy task, since the number of possible combinations grows exponentially with the number of possible parameters to be considered. This problem is usually overcome by assuming simplified models based on experience or using heuristic approaches, which are computationally very expensive. In this paper, a method to obtain a pseudo-optimal parameterization using the maximum likelihood method is presented. The proposed algorithm automatically selects the parameters which minimize the Akaike Information Criterion within an iterative scheme, including one parameter at a time based on a score perturbation criteria. The process is repeated until no further improvement in the objective function is achieved. The proposed method is applied for the adjustment of monthly maximum significant wave height at different locations around the Atlantic coast and results are compared with those obtained using an existing heuristic approach, showing an important reduction in computational time and comparable results in terms of fitting quality. (copyright) 2010 Elsevier Ltd.