We test the hypothesis that abrupt cessation of solar wind driving results in a different recovery profile for Dst than does a slow cessation. The difference arises when abrupt cessation of convection causes a large portion of the asymmetric ring current to be trapped, whereas continued, weakened convection permits a rapid initial loss of ring current particles through the dayside magnetopause. Specifically, we compare the initial recovery of the hourly Dst index for storms with gradual versus abrupt northward turning of the interplanetary magnetic field (IMF). We consider only storms with minimum Dst between -150 nT and -300 nT. We show that storms with abrupt northward turnings show the same recovery in the first 6 hours or slightly more recovery than do the storms with gradual northward turnings. Our results contradict the hypothesis that the rate of northward turning (i.e., shutoff of convection) largely determines the initial rate of recovery in Dst.