In this article we build a model of the CpG dinucleotide substitution rate and use it to challenge the claim that, that rate underwent a sudden mammalian-specific increase approximately 90 million years ago. The evidence supporting this hypothesis comes from the application of a model of neutral substitution rates able to account for elevated CpG dinucleotide substitution rates. With the initial goal of improving that models accuracy, we introduced a modification enabling us to account for boundary effects arising by the truncation of the Markov field, as well as improving the optimization procedure required for estimating the substitution rates.