Given a set of grouped survival data, least squares estimates are proposed for the parameters of four survival distributions that can be fit: exponential, linear hazard, Gompertz and Weibull. Sample estimates of the hazard function are utilized in the least squares procedures and a method is given for selecting a distribution for further investigation based on the likelihood under the four survival models. A Monte Carlo study demonstrated that the least squares estimates are nearly as efficient as maximum likelihood when the sample size is 50 or more. The methods are applied to survival data for 112 patients with plasma cell myeloma.