In recent work, Bruce Hayes and Kie Zuraw (HZ) have defended the generalization that the rates of application of a variable phonological process on four underlying forms that differ along two independent phonological dimensions can be fitted on two shifted sigmoids at shared abscissas. HZ observe that the popular Maximum Entropy (ME) grammars satisfy this generalization. This paper shows that, within harmony-based phonology, there are virtually no other options. In the sense that a harmony-based grammar satisfies HZ's generalization if and only if it is either a ME grammar or else it can be construed as a ME grammar through a transformation of the constraints. This constraint transformation is plausibly innocuous in the daily business of phonological analysis, where constraint violations are usually small numbers. In conclusion, this paper shows that HZ's generalization provides sort of an axiomatic justification of ME within harmony-based phonology.