The usual calculation of Dreicer [Phys. Rev. 115 , 238 (1959); 117 , 329 (1960)] generation of runaway electrons assumes that the plasma is in a steady state. In a tokamak disruption this is not necessarily true since the plasma cools down quickly and the collision time for electrons at the runaway threshold energy can be comparable to the cooling time. The electron distribution function then acquires a high-energy tail which can easily be converted to a burst of runaways by the rising electric field. This process is investigated and simple criteria for its importance are derived. If no rapid losses of fast electrons occur, this can be a more important source of runaway electrons than ordinary Dreicer generation in tokamak disruptions.