Measurement-based load modeling, especially in the presence of new loads such as power electronics-interfaced loads and electric vehicles with fast dynamics, requires fast-converging algorithms that provide the model parameters with high reliability. In the current practice, all or only a subset of the parameters of an aggregated load model are estimated using iterative optimization algorithms. Thus, the identification problem either has a high dimension, which leads to a large variance for the estimated parameters, or does not include a subset of the parameters with low sensitivity. In this paper, an efficient approach for the estimation of the composite load model parameters is proposed that addresses these issues. This method partitions the parameters into two subsets; one that appears nonlinearly in the model output, and a second set that affects the outputs linearly. Then, the optimization is performed only with respect to the nonlinear set, with the linear parameters treated as explicit functions of the nonlinear ones. This approach effectively reduces the dimension of the search space since it only includes the nonlinear parameters in the optimization, and also includes the linear parameters by computing them using linear regression at each iteration. These features lead to a much faster convergence while all of the composite load model parameters are estimated reliably. Experimental and simulation data are presented to demonstrate the performance of the proposed method.