A new method for determining least squares estimators for certain classes of non- linear models is discussed. The method is an extension of a variable projection method of Scolnik (1970), and involves the minimization of a modified functional. The feature of minimizing this modified functional is that for a certain class of non-linear models, called the constant-coefficients case, only one half the parameters are involved initially. To find the estimators of the remaining parameters is straight forward and relatively easy. This new two step-procedure is shown to be equivalent to the over-all least squares procedure. We also discuss the case of a class of models called the variable coefficients class. For this case, we formulate a new algorithm for determining the estimators which makes use of approximate confidence regions for the parameters.