The Collaborative International Dictionary of English v.0.48:

Qualify \Qual"i*fy\, v. t. [imp. & p. p. Qualified; p. pr. &
   vb. n. Qualifying.] [F. qualifier, LL. qualificare, fr. L.
   qualis how constituted, as + -ficare (in comp.) to make. See
   Quality, and -Fy.]
   1. To make such as is required; to give added or requisite
      qualities to; to fit, as for a place, office, occupation,
      or character; to furnish with the knowledge, skill, or
      other accomplishment necessary for a purpose; to make
      capable, as of an employment or privilege; to supply with
      legal power or capacity.
      [1913 Webster]

            He had qualified himself for municipal office by
            taking the oaths to the sovereigns in possession.
                                                  --Macaulay.
      [1913 Webster]

   2. To give individual quality to; to modulate; to vary; to
      regulate.
      [1913 Webster]

            It hath no larynx . . . to qualify the sound. --Sir
                                                  T. Browne.
      [1913 Webster]

   3. To reduce from a general, undefined, or comprehensive
      form, to particular or restricted form; to modify; to
      limit; to restrict; to restrain; as, to qualify a
      statement, claim, or proposition.
      [1913 Webster]

   4. Hence, to soften; to abate; to diminish; to assuage; to
      reduce the strength of, as liquors.
      [1913 Webster]

            I do not seek to quench your love's hot fire,
            But qualify the fire's extreme rage.  --Shak.
      [1913 Webster]

   5. To soothe; to cure; -- said of persons. [Obs.]
      [1913 Webster]

            In short space he has them qualified. --Spenser.
      [1913 Webster]

   Syn: To fit; equip; prepare; adapt; capacitate; enable;
        modify; soften; restrict; restrain; temper.
        [1913 Webster]

WordNet (r) 3.0 (2006):

qualifying
    n 1: the grammatical relation that exists when a word qualifies
         the meaning of the phrase [syn: modification,
         qualifying, limiting]
    2: success in satisfying a test or requirement; "his future
       depended on his passing that test"; "he got a pass in
       introductory chemistry" [syn: passing, pass,
       qualifying] [ant: failing, flunk]

Moby Thesaurus II by Grady Ward, 1.0:

20 Moby Thesaurus words for "qualifying":
   altering, assuasive, bounding, extenuating, extenuatory, lenitive,
   limitative, limiting, mitigating, mitigative, mitigatory,
   modificatory, modifying, modulatory, palliative, qualificative,
   qualificatory, restricting, restrictive, softening