Stabilisation of sawteeth due to α-particles or ion cyclotron resonance heating (ICRH) is well-established experimentally and understood theoretically [1]: it arises from third adiabatic invariant conservation for trapped fast ions precessing around the torus in a time shorter than the m = 1 internal kink mode period. This mode has frequency ω ~ ω*i, the bulk ion diamagnetic frequency, and so stabilisation requires ωDh ~> ω*i, where ωDh is the fast ion precession frequency. In JET this condition is easily satisfied by ICRH ions with energies E ~ MeV; for NBI ions with E <~ 100keV it is generally only marginally satisfied. Clear evidence for NBI stabilisation of sawteeth has nevertheless been found, for example in TEXTOR [2]. In recent JET discharges, with beam injection energies of up to 140keV, sawtooth periods τsaw ~ 500ms have been observed. To investigate the processes determining τsaw in these discharges we have used a transport code (PRETOR) to implement a model that was developed to predict the sawtooth period in ITER [3] and has been applied successfully to TCV [4]. The value of τsaw in any Next Step device is likely to have a strong bearing on plasma performance: for example, crashes following long sawtooth periods can give rise to seed magnetic islands that trigger neoclassical tearing modes [5].