We used an rf solenoid to study the widths of rf spin resonances with both bunched and unbunched beams of 1.85 GeV/c polarized deuterons stored in the COSY synchrotron. With the unbunched beam at different fixed rf-solenoid frequencies, we observed only partial depolarization near the resonance. However, the bunched beam's polarization was almost fully flipped; moreover, its resonance was much narrower. We then used Chao's recent equations to explain this behavior and to calculate the polarization's dependence on various rf-solenoid and beam parameters. Our data and calculations indicate that a bunched deuteron beam's polarization can behave as if the beam has zero momentum spread.