The globalization of markets and geographic dispersion of production facilities, combined with a heavy outsourcing of supply chain processes, have substantially increased the exposure of supply chains to supply lead-times of long and uncertain nature. In this paper, we study the potential use of two contingency strategies on top of the conventionally used time buffer—statically planned safety lead-time (SL)—approach to deal with the lead-time uncertainty. These are (1) the ex-ante planning for disruption safety stock (DSS) to be released when a “disruption” (in this case, late delivery of the order) occurs; and (2) the ex-post dynamic emergency response (DER), which dynamically decides on the timing and size of an emergency order to be placed. Our work elaborates on the optimal parameter setting for these strategies, compares their added values when used to complement the traditional SL approach, and examines how the use of the contingency strategies affects the SL and corresponding cycle length of a periodic review system. Our research finds that: (1) the above contingency strategies reduce the reliance on the SL and are cost effective when the coefficient of variation (CV) of the uncertain lead-time is high; (2) it is important to re-optimize the SL to account for the contingency plans; and (3) re-optimization of the cycle length to account for the presence of the contingency responses, as opposed to using an EOQ-determined cycle length, does not significantly improve the cost performance. However, such re-optimization does well in the SL approach when the CV of the uncertain lead-time is high.