The estimation of the parameters of dosage response curves by the standard probit method is an iterative process beginning with approximations to the parameters and using one or more cycles of computations to “improve” these estimates until they converge. The present paper gives a table and method for computing the maximum likelihood solution which converges more rapidly than the standard probit method. A procedure is presented for obtaining more accurate initial approximations, and the problem of the bias of the maximum likelihood estimates in small samples is considered.