The Jeans equations give the second moments or stresses required to su
pport a stellar population against a gravity field. A general solution
of the Jeans equations for arbitrary axisymmetric scale-free densitie
s in flattened scale-free potentials is given. A two-parameter subset
of the solution for the second moments for the self-consistent density
of the power-law models, which have exactly spheroidal equipotentials
, is examined in detail, In the spherical limit, the potential of thes
e models reduces to that of the singular power-law spheres. We build t
he physical three-integral distribution functions that correspond to t
he flattened stellar components. Next, we attack the problem of findin
g distribution functions associated with the Jeans solutions in flatte
ned scale-free potentials, The third or partial integral introduced by
de Zeeuw, Evans & Schwarzschild for Binney's model is generalized to
thin and near-thin orbits moving in arbitrary axisymmetric scale-free
potentials. The partial integral is a modification of the total angula
r momentum. For the self-consistent power-law models, we show how this
enables the construction of simple three-integral distribution functi
ons. The connection between these approximate distribution functions a
nd the Jeans solutions is discussed in some detail.