We will first review what is know of metrics on the 2-sphere whose geodesic flow is ergodic: they all involve use of "focusing caps". We show that under arbitrarily small perturbations to the focusing cap, one can create metrics whose geodesic flow contain elliptic (stable) periodic orbits and hence are non-ergodic. We use a version of Newhouse's argument involving a one-parameter family of horseshoes to prove this result.