We present a new class of spherical galactic models with mild central cusps whose distribution function (DF) and intrinsic velocity dispersion (IV) can be represented analytically in a unified way in terms of hypergeometric functions for a large number of parameters. This allows an easy comparison of these quantities for models having varying degrees of central cuspiness or outer density falloff. In particular, we study the models for the innermost regions of galaxies harbouring mild cuspy centers with or without supermassive black holes (SBH). Important properties infered from the observed behaviour of the velocity dispersions can be reproduced.