The Collaborative International Dictionary of English v.0.48:

Discomposure \Dis`com*po"sure\ (?; 135), n.
   1. The state of being discomposed; disturbance; disorder;
      agitation; perturbation.
      [1913 Webster]

            No discomposure stirred her features. --Akenside.
      [1913 Webster]

   2. Discordance; disagreement of parts. [Obs.] --Boyle.
      [1913 Webster]

WordNet (r) 3.0 (2006):

discomposure
    n 1: anxious embarrassment [syn: discomfiture, discomposure,
         disconcertion, disconcertment]
    2: a temperament that is perturbed and lacking in composure
       [ant: calm, calmness, composure, equanimity]