Most bounds on the stability region of Aloha give necessary and sufficient conditions for the stability of an arrival rate vector under a specific contention probability (control) vector.  But such results do not yield easy-to-check bounds on the overall Aloha stability region because they potentially require checking membership in an uncountably infinite number of sets parameterized by each possible control vector.  In this paper we consider an important specific inner bound on Aloha that has this property of difficulty to check membership in the set.  We provide easy-to-check inner and outer bounds on this set using inscribed and circumscribed ellipsoids for a related convex set.  We also study the set of controls that stabilize a fixed arrival rate vector; this set is shown to be convex and we give a maximum volume inscribed ellipsoid for two users.