  We present a systematic analysis of the constraints $\sigma_\gamma$ on the
mass profile slope $\gamma$ obtainable when fitting a singular power-law
ellipsoid model to a typical strong lensing observation of an extended source.
These results extend our previous analysis of circular systems, Paper I. We
draw our results from 676 mock observations covering a range of image
configurations, each created with a fixed signal to noise ratio $S=100$ in the
images. We analyse the results using a combination of theory and a simplified
model which identifies the contribution to the constraints of the individual
fluxes and positions in each of the lensed images. The main results are: 1. For
any lens ellipticity, the constraints $\sigma_\gamma$ for two image systems are
well described by the results of Paper I, transformed to elliptical
coordinates; 2. We derive an analytical expression for $\sigma_\gamma$ for
systems with the source aligned with the axis of the lens; 3. For both
two-image systems and aligned systems, $\sigma_\gamma$ is limited by the flux
uncertainties; 4. The constraints for off-axis four-image systems are a factor
of two to eight better, depending on source size, than for two-image systems,
and improve with increasing lens ellipticity. We show that the constraints on
$\gamma$ in these systems derive from the complementary positional information
of the images alone, without using flux. The complementarity improves as the
offset of the source from the axis increases, such that the best constraints
$\sigma_\gamma<0.01$, for $S=100$, occur when the source approaches the
caustic.
