A striking observation from both Cascadia and Japan is that the tremor associated with slow slip often migrates along strike at speeds close to 10 km/d but updip and downdip at speeds approaching 100 km/h. In this paper I adopt the view that the friction law appropriate for these regions is unknown, and I ask what constraints the observed behavior places on the friction law that must be operating. A simple relation, relying only on kinematics and elasticity, states that for a moving front the ratio of propagation speed to slip speed equals the ratio of the elastic shear modulus to the peak-to-residual stress drop at the front. Thus, larger propagation speeds require some combination of larger slip speeds and smaller peak-to-residual stress drops. As a proof of concept I design a two-state-variable friction law in which the strength drop associated with the main laterally propagating front, moving into a region that has not slipped since the last slow event, is much larger than that at the secondary fronts developing on the active slip surface. Preliminary numerical simulations demonstrate that this law can generate secondary fronts that propagate updip and downdip more than 2 orders of magnitude faster than, and even at some distance from, the main lateral front, as has been observed in Cascadia and Japan.