The Collaborative International Dictionary of English v.0.48:

Self-assured \Self`-as*sured`\, a.
   Assured by or of one's self; self-reliant; complacent.
   [1913 Webster]

WordNet (r) 3.0 (2006):

self-assured
    adj 1: showing poise and confidence in your own worth; "hardly
           more than a boy but firm-knit and self-confident" [syn:
           self-assured, self-confident]

Moby Thesaurus II by Grady Ward, 1.0:

43 Moby Thesaurus words for "self-assured":
   arrogant, assured, balanced, cocksure, collected, composed,
   confident, convinced, decided, determined, equanimous,
   equilibrious, hubristic, levelheaded, overconfident, oversure,
   overweening, persuaded, poised, pompous, positive, proud,
   reassured, recollected, sanguine, secure, self-confident,
   self-controlled, self-important, self-possessed, self-reliant,
   self-restrained, self-satisfied, smug, sure, together, unafraid,
   undoubtful, undoubting, unfaltering, unhesitating, unwavering,
   well-balanced