  Both numerical simulations and observational evidence indicate that the outer
regions of galaxies and dark matter haloes are typically mildly to
significantly radially anisotropic. The inner regions can be significantly
non-isotropic, depending on the dynamical formation and evolution processes. In
an attempt to break the lack of simple dynamical models that can reproduce this
behaviour, we explore a technique to construct dynamical models with an
arbitrary density and an arbitrary anisotropy profile. We outline a general
construction method and propose a more practical approach based on a
parameterized anisotropy profile. This approach consists of fitting the density
of the model with a set of dynamical components, each of which have the same
anisotropy profile. Using this approach we avoid the delicate fine-tuning
difficulties other fitting techniques typically encounter when constructing
radially anisotropic models. We present a model anisotropy profile that
generalizes the Osipkov-Merritt profile, and that can represent any smooth
monotonic anisotropy profile. Based on this model anisotropy profile, we
construct a very general seven-parameter set of dynamical components for which
the most important dynamical properties can be calculated analytically. We use
the results to look for simple one-component dynamical models that generate
simple potential-density pairs while still supporting a flexible anisotropy
profile. We present families of Plummer and Hernquist models in which the
anisotropy at small and large radii can be chosen as free parameters. We also
generalize these two families to a three-parameter family that
self-consistently generates the set of Veltmann potential-density pairs.
(Abridged...)
