The zero lower bound (ZLB) constraint on interest rates makes speed limit policies (SLPs)---policies aimed at stabilizing the output growth---less effective. Away from the ZLB, the history dependence induced by a concern for output growth stabilization improves the inflation-output tradeoff for a discretionary central bank. However, in the aftermath of a deep recession with a binding ZLB, a central bank with an objective for output growth stabilization aims to engineer a more gradual increase in output than under the standard discretionary policy. The anticipation of a more restrained recovery exacerbates the declines in inflation and output when the lower bound is binding.