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]