The Collaborative International Dictionary of English v.0.48:

Insufficiency \In`suf*fi"cien*cy\, n. [L. insufficientia: cf. F.
   insuffisance, whence OE. insuffisance. See Insufficient.]
   [1913 Webster]
   1. The quality or state of being insufficient; lack of
      sufficiency; deficiency; inadequateness; as, the
      insufficiency of provisions, of an excuse, etc.
      [1913 Webster]

            The insufficiency of the light of nature is, by the
            light of Scripture, . . . fully supplied. --Hooker.
      [1913 Webster]

   2. Lack of power or skill; inability; incapacity;
      incompetency; as, the insufficiency of a man for an
      office.
      [1913 Webster]

WordNet (r) 3.0 (2006):

insufficiency
    n 1: a lack of competence; "pointed out the insufficiencies in
         my report"; "juvenile offenses often reflect an inadequacy
         in the parents" [syn: insufficiency, inadequacy]
    2: (pathology) inability of a bodily part or organ to function
       normally
    3: lack of an adequate quantity or number; "the inadequacy of
       unemployment benefits" [syn: insufficiency, inadequacy,
       deficiency] [ant: adequacy, sufficiency]

Moby Thesaurus II by Grady Ward, 1.0:

96 Moby Thesaurus words for "insufficiency":
   arrear, arrearage, arrears, asymmetry, baseness, contrariety,
   daintiness, decline, defalcation, default, defectiveness,
   deficiency, deficit, delicacy, delinquency, difference,
   diminutiveness, disability, disablement, disequilibrium, disparity,
   disproportion, disqualification, dissatisfactoriness, exiguity,
   exiguousness, failure, falling short, fewness, heterogeneity,
   imbalance, imbecility, imperfection, inability, inadequacy,
   inadmissibility, incapability, incapacitation, incapacity,
   incompetence, incompetency, inconsequentiality, inconsiderableness,
   indefensibility, inefficiency, ineptitude, inequality, inequity,
   infancy, inferiority, injustice, insignificance, intolerability,
   irregularity, legal incapacity, littleness, maladroitness,
   meagerness, meanness, mediocrity, minority, minuteness,
   moderateness, nonuniformity, objectionability, odds, overbalance,
   pettiness, picayunishness, puniness, scantiness, shabbiness,
   short measure, shortage, shortcoming, shortfall, slightness, slump,
   smallness, subnormality, tininess, triviality, unacceptability,
   unbalance, underage, undesirability, unevenness,
   unfair discrimination, unfitness, unimportance, unsatisfactoriness,
   unskillfulness, unsuitability, untenability, vulgarity, wardship



Bouvier's Law Dictionary, Revised 6th Ed (1856):

INSUFFICIENCY. What is not competent; not enough.