WordNet (r) 3.0 (2006):

open-and-shut
    adj 1: so obvious as to be easily solved or decided; "an open-
           and-shut case"

Moby Thesaurus II by Grady Ward, 1.0:

53 Moby Thesaurus words for "open-and-shut":
   apparent, ascertained, assured, attested, certified, clear,
   clear as crystal, crystal-clear, decided, determinate, determined,
   discernible, distinct, established, evident, explicit, express,
   fixed, guaranteed, in the bag, indisputable, indubitable,
   made sure, manifest, nailed down, noticeable, observable, obvious,
   on ice, palpable, patent, perceivable, perceptible, perspicuous,
   plain, plain as day, proved, secure, seeable, self-evident,
   self-explaining, self-explanatory, set, settled, stated,
   straightforward, tangible, tested, to be seen, tried, unmistakable,
   visible, warranted