  We present a new non-parametric Jeans code, GravSphere, that recovers the
density $\rho(r)$ and velocity anisotropy $\beta(r)$ of spherical stellar
systems, assuming only that they are in a steady-state. Using a large suite of
mock data, we confirm that with only line-of-sight velocity data, GravSphere
provides a good estimate of the density at the projected stellar half mass
radius, $\rho(R_{1/2})$, but is not able to measure $\rho(r)$ or $\beta(r)$,
even with 10,000 tracer stars. We then test three popular methods for breaking
this $\rho-\beta$ degeneracy: using multiple populations with different
$R_{1/2}$; using higher order `Virial Shape Parameters' (VSPs); and including
proper motion data.
  We find that two populations provide an excellent recovery of $\rho(r)$
in-between their respective $R_{1/2}$. However, even with a total of $\sim
7,000$ tracers, we are not able to well-constrain $\beta(r)$ for either
population. By contrast, using 1000 tracers with higher order VSPs we are able
to measure $\rho(r)$ over the range $0.5 < r/R_{1/2} < 2$ and broadly constrain
$\beta(r)$. Including proper motion data for all stars gives an even better
performance, with $\rho$ and $\beta$ well-measured over the range $0.25 <
r/R_{1/2} < 4$.
  Finally, we test GravSphere on a triaxial mock galaxy that has axis ratios
typical of a merger remnant, $[1:0.8:0.6]$. In this case, GravSphere can become
slightly biased. However, we find that when this occurs the data are poorly
fit, allowing us to detect when such departures from spherical symmetry become
problematic.
