This paper provides a simple general procedure to construct self-consistent spherical equilibrium models of stellar systems populated by stars in quasi-circular orbits. The focus on Maxwellian-like distributions in the relevant velocity space and the use of the epicyclic expansion allow us to work with physically intuitive models. Explicit solutions for a sequence of distribution functions with density distribution close to that of isochrone models are produced with varying degrees of pressure anisotropy. These results are meant to be the starting point for extensive stability analyses, and they may also be of interest for the construction of quantities such as projected velocity dispersion and line-of-sight-velocity profiles for comparison with observations of elliptical galaxies.