  A method is given for calculating the strict minimum message length (SMML)
estimator for 1-dimensional exponential families with continuous sufficient
statistics. A set of $n$ equations are found that the $n$ cut-points of the
SMML estimator must satisfy. These equations can be solved using Newton's
method and this approach is used to produce new results and to replicate
results that C. S. Wallace obtained using his boundary rules for the SMML
estimator. A rigorous proof is also given that, despite being composed of step
functions, the posterior probability corresponding to the SMML estimator is a
continuous function of the data.
