Synonyms for Tight-laced (same or very similar meaning)
WordNet sense 1 (exaggeratedly proper):
priggish, prim, prissy, prudish, puritanical, straitlaced, square-toed, straightlaced, straight-laced, strait-laced, Victorian
WordNet sense 2 (marked by suitability or rightness or appropriateness):
proper
From the ODE community, based on WordNet
add/edit