Many gamma-ray bursts (GRBs) have been observed with the Burst Alert Telescope and X-Ray Telescope of the Swift satellite. The successive "pulses" of these GRBs end with a fast decline and a fast spectral softening, until they are overtaken by another pulse or the last pulse's decline is overtaken by a less rapidly varying "afterglow." The fast-decline phase has been attributed, in the currently explored standard fireball model of GRBs, to "high-latitude" synchrotron emission from a collision of two conical shells. This high-latitude emission does not explain the observed spectral softening. In contrast, the temporal behavior and the spectral evolution during the fast-decline phase agree with the predictions of the cannonball model for GRBs.