This paper investigates the relationship between variability and lexic
ality on the one hand and sound change on the other within the theory
of Lexical Phonology. The former leads to the proposal of the Optional
ity Constraint (OC), which prohibits the application of optional rules
in the lexical module. The constraint is found to be violated at the
word level. The violation of OC as well as of other lexical modular pr
inciples is accounted for by the help of a new licensing principle, ca
lled the Polarity Principle. This allows for interacting modules to ha
ve different properties of representation and rule application at thei
r opposite ends. The OC leads to a resolution of the Neogrammarian Con
troversy, that is consonant with the standard assumption concerning so
und change, namely, the inherent relation between the latter and varia
bility.