The problems of one-dimensional and two-dimensional (1-D and 2-D) parameter estimation based on the iterative quadratic maximum likelihood (IQML) algorithm are considered. For the 1-D frequency or source direction estimation problem, the inefficiency of two existing versions of the algorithm is addressed. An improved algorithm is obtained by using a new consistent nontriviality constraint. In addition, the IQML algorithm is applied to solve the 2-D frequency estimation problem. Given the estimates of 1-D frequency parameters in each of the two dimensions, a sufficient condition for consistent parameter pairing is provided. Numerical results are given to demonstrate the improvement gained by the proposed work.