WordNet (r) 3.0 (2006):

turn down
    v 1: refuse to accept; "He refused my offer of hospitality"
         [syn: refuse, reject, pass up, turn down,
         decline] [ant: accept, have, take]
    2: refuse entrance or membership; "They turned away hundreds of
       fans"; "Black people were often rejected by country clubs"
       [syn: reject, turn down, turn away, refuse] [ant:
       admit, allow in, intromit, let in]
    3: reject with contempt; "She spurned his advances" [syn:
       reject, spurn, freeze off, scorn, pooh-pooh,
       disdain, turn down]
    4: take a downward direction; "The economy finally turned down
       after a long boom"
    5: make lower or quieter; "turn down the volume of a radio"
       [syn: turn down, lower, lour]

Moby Thesaurus II by Grady Ward, 1.0:

54 Moby Thesaurus words for "turn down":
   be unmoved, be unwilling, beg off, convert, decline,
   decline to accept, disagree, disallow, disapprove, disclaim,
   dismiss, dissent, evert, hold out against, introvert, intussuscept,
   invaginate, inverse, invert, negate, negative, not buy,
   not consent, not hear of, not think of, pronate, refuse,
   refuse consent, reject, reprobate, repudiate, resist entreaty,
   resist persuasion, resupinate, reverse, revolve, rotate, say nay,
   say no, spurn, stand aloof, supinate, transpose, turn about,
   turn around, turn in, turn inside out, turn out, turn over,
   turn the scale, turn the tables, turn upside down, vote nay,
   vote negatively