  We investigate binary lenses with $1/r^n$ potentials in the asymmetric case
with two lenses with different indexes $n$ and $m$. These kinds of potentials
have been widely used in several contexts, ranging from galaxies with halos
described by different power laws to lensing by wormholes or exotic matter. In
this paper, we present a complete atlas of critical curves and caustics for
mixed binaries, starting from the equal-strength case, and then exploring
unequal-strength systems. We also calculate the transitions between all
different topology regimes. Finally we find some useful analytic approximations
for the wide binary case and for the extreme unequal-strength case.
