In multiparameter situations there are important problems of convergence in the solution of maximum likelihood iterative equations. Convergence may be critically dependent on the initial parameter estimates employed. These problems are indicated specifically for a model of exponentially-distributed lifetimes where the reciprocal of the exponential parameter is linearly dependent on various regressor variables. A strategy is suggested based on alternative use of observed or expected values for the sample second derivative of the log likelihood. For the examples shown the initial parameter estimates correspond to no effect for the regressor variables, this being equivalent in some cases to making an unweighted fit to the data.