The Collaborative International Dictionary of English v.0.48:

Andantino \An`dan*ti"no\, a. [It., dim. of andante.] (Mus.)
   Rather quicker than andante; between that allegretto.
   [1913 Webster]

   Note: Some, taking andante in its original sense of "going,"
         and andantino as its diminutive, or "less going,"
         define the latter as slower than andante.
         [1913 Webster]

WordNet (r) 3.0 (2006):

andantino
    adj 1: (of tempo) moderately fast