Synonyms for Puritanical (same or very similar meaning)
WordNet sense 1 (exaggeratedly proper):
priggish, prim, prissy, prudish, straitlaced, square-toed, straightlaced, straight-laced, strait-laced, tight-laced, VictorianWordNet sense 2 (marked by suitability or rightness or appropriateness):
properWordNet sense 3 (morally rigorous and strict):
blue, puritan, puritanicWordNet sense 4 (characterized by strictness, severity, or restraint):
strict, nonindulgentFrom the ODE community, based on WordNetadd/edit