Square-integrable functions whose Fourier transforms have compact support in the interval [-pi, pi] can be recovered from their samples on a set of points called a complete interpolating sequence (CIS). A CIS is a minimal set in the sense that it has minimal density and recovery fails if a single point is removed from the CIS. The integers are the best-known example of a CIS, leading to uniform sampling and the classical Sampling Theorem. We investigate whether all CISs are 'created equal', or if some CISs can 'resolve' larger spaces of bandlimited functions than others.