  We present a simple and efficient anisotropic generalization of the
semi-isotropic (two-integral) axisymmetric Jeans formalism which is used to
model the stellar kinematics of galaxies. The following is assumed: (i) a
constant mass-to-light ratio M/L and (ii) a velocity ellipsoid that is aligned
with cylindrical coordinates (R,z) and characterized by the classic anisotropy
parameter beta_z=1-sigma_z^2/sigma_R^2. Our simple models are fit to SAURON
integral-field observations of the stellar kinematics for a set of fast-rotator
early-type galaxies. With only two free parameters (beta_z and the inclination)
the models generally provide remarkably good descriptions of the shape of the
first (V) and second (V_rms=sqrt{V^2+sigma^2}) velocity moments, once a
detailed description of the surface brightness is given. This is consistent
with previous findings on the simple dynamical structure of these objects. With
the observationally-motivated assumption that beta_z>0, the method is able to
recover the inclination. The technique can be used to determine the dynamical
mass-to-light ratios and angular momenta of early-type fast-rotators and spiral
galaxies, especially when the quality of the data does not justify more
sophisticated modeling approaches. This formalism allows for the inclusion of
dark matter, supermassive black holes, spatially varying anisotropy, and
multiple kinematic components.
