This paper outlines a working technique for obtaining maximum likelihood estimates for the parameters of a regression curve [epsilon](Y) =[alpha] - [beta]1[RHO]1x - [beta]2[RHO]2x; O<[RHO]1<[RHO]2<1. This technique is derived by using a combination of Stevens'' and Richards'' methods applied to the double exponential case. The method has the advantages of giving a best estimate if one exists and clearly revealing cases in which a best estimate in the desired region does not exist. It seems also readily extendable to multiple exponential regression. Two examples are given, one in which convergence is obtained and one which has no best estimate in the desired region.