During a recent reversed toroidal field (BT) campaign at the Joint European Torus (JET), experiments were performed to investigate the effect on sawteeth of neutral beam injection (NBI)-driven toroidal plasma rotation counter to the direction of the toroidal plasma current and BT. A power scan at constant density has permitted analytical continuation, into the reversed BT domain, of previous experiments with forward field and hence corotation. Earlier JET results were confirmed, indicating that counter-NBI results in sawtooth periods shorter than in the Ohmic regime. This study has demonstrated that, whereas with co-NBI the sawtooth period increases with power, with counter-NBI the sawtooth period initially decreases with power passing through a minimum at 4 MW. Clearly this trend also manifests itself in terms of the toroidal plasma rotation, for which a minimum is observed for counter-rotation frequency 3 kHz. Sawteeth smaller than Ohmic sawteeth are found to be easier to obtain with perpendicular counter-NBI, for which heating penetrates deeper into the core. The sign and magnitude of the toroidal rotation, the penetration of heating to the electrons, and the peaking of the fast-ion pressure profile in the core may all play an important role in modifying the sawtooh period.