The Collaborative International Dictionary of English v.0.48:

anaesthetize \a*n[ae]s"the*tize\, anesthetize \a*nes"the*tize\,
   ([a^]n*[e^]s"th[-e]*t[imac]z), v. t. (Med.)
   To produce anesthesia by an an[ae]sthetic. --Encyc. Brit.
   [1913 Webster + AS]

The Collaborative International Dictionary of English v.0.48:

anesthetize \anesthetize\ v. t.
   To cause to become unconscious by administration of an
   anaesthetic agent. [Also spelled anaesthetize.]

   Syn: put to sleep, put under, put out.
        [WordNet 1.5 +PJC]

WordNet (r) 3.0 (2006):

anesthetize
    v 1: administer an anesthetic drug to; "The patient must be
         anesthetized before the operation"; "anesthetize the gum
         before extracting the teeth" [syn: anesthetize,
         anaesthetize, anesthetise, anaesthetise, put under,
         put out] [ant: bring around, bring back, bring
         round, bring to]

Moby Thesaurus II by Grady Ward, 1.0:

68 Moby Thesaurus words for "anesthetize":
   KO, abate, allay, alleviate, appease, assuage, bedaze, benumb,
   besot, blunt, chloroform, coldcock, cushion, deaden,
   deaden the pain, desensitize, diminish, dope, drug, dull, ease,
   ease matters, entrance, etherize, foment, freeze, give relief,
   hypnotize, kayo, knock out, knock senseless, knock stiff,
   knock unconscious, lay, lay out, lessen, lull, lull to sleep,
   magnetize, mesmerize, mitigate, mollify, narcotize, numb, obtund,
   pad, palliate, palsy, paralyze, poultice, pour balm into,
   pour oil on, put to sleep, put under, reduce, relieve,
   rock to sleep, salve, sedate, slacken, slake, soften, soothe, stun,
   stupe, stupefy, subdue, trance