The H-mode power threshold has a weak but positive dependence when the ion drift is away from the X-point, in contrast to the nearly linear dependence when the ion drift is toward the X-point. This indicates that geometry plays an important role in the H-mode power threshold scaling. A simple model of the drift effect failed to predict this behaviour, but successfully predicted the sign change of gas puffing and low X-point height on the power threshold. The difference between the threshold power required for sawtooth and non-sawtooth-triggered transitions can be substantial. This effect may contribute to the observed B scaling of the H-mode power threshold.