We recently used a prototype rf dipole magnet to study the spin flipping of a 669 MeV horizontally polarized electron beam stored in the presence of a nearly full Siberian snake in the new MIT-Bates storage ring. We flipped the spin by ramping the rf dipole's frequency through an rf-induced depolarizing resonance. After optimizing the frequency ramp parameters, we used multiple spin flipping to measure a spin-flip efficiency of 94.5±2.5%. The spin-flip efficiency was apparently limited by the field strength in the air-core prototype rf dipole magnet. This unexpectedly high efficiency indicates that very efficient spin flipping of the ring's stored polarized electron beam should be possible using the much stronger ferrite spin flipper, which is now being built by the University of Michigan's Spin Physics Center.