The Collaborative International Dictionary of English v.0.48:

Puritanic \Pu`ri*tan"ic\, Puritanical \Pu`ri*tan"ic*al\, a.
   1. Of or pertaining to the Puritans, or to their doctrines
      and practice.
      [1913 Webster]

   2. Precise in observance of legal or religious requirements;
      strict; overscrupulous; rigid; -- often used by way of
      reproach or contempt.
      [1913 Webster]

            Paritanical circles, from which plays and novels
            were strictly excluded.               --Macaulay.
      [1913 Webster]

            He had all the puritanic traits, both good and evil.
                                                  --Hawthorne.
      [1913 Webster]

WordNet (r) 3.0 (2006):

puritanical
    adj 1: of or relating to Puritans or Puritanism
    2: exaggeratedly proper; "my straitlaced Aunt Anna doesn't
       approve of my miniskirts" [syn: priggish, prim, prissy,
       prudish, puritanical, square-toed, straitlaced,
       strait-laced, straightlaced, straight-laced, tight-
       laced, victorian]
    3: morally rigorous and strict; "the puritan work ethic";
       "puritanic distaste for alcohol"; "she was anything but
       puritanical in her behavior" [syn: blue(a), puritanic,
       puritanical]

Moby Thesaurus II by Grady Ward, 1.0:

93 Moby Thesaurus words for "puritanical":
   Albigensian, Catharist, Franciscan, Quakerish, Sabbatarian,
   Trappist, Victorian, Waldensian, abstinent, anchoritic, ascetic,
   austere, bigoted, censorious, choicy, choosy, conscientious,
   creedbound, critical, demure, discriminating, discriminative,
   dogmatic, dour, eremitic, evangelical, exacting, fastidious, firm,
   flagellant, fundamentalist, hard, hidebound, hyperorthodox,
   impliable, inexorable, inflexible, iron, ironbound, ironclad,
   ironhanded, literalist, literalistic, mendicant, meticulous,
   mid-Victorian, muscle-bound, narrow, obdurate, obstinate,
   old-maidish, orthodox, overmodest, particular, perfectionistic,
   picky, precise, precisianist, precisianistic, priggish, prim,
   procrustean, prudish, punctilious, purist, puristic, puritan,
   puritanic, relentless, rigid, rigorist, rigoristic, rigorous,
   rockbound, sanctimonious, scrupulous, selective, self-denying,
   sensitive, smug, staunch, stiff, stiff-necked, straightlaced,
   straitlaced, strict, stubborn, stuffy, unbending, uncompromising,
   unrelenting, unyielding, wedded to poverty