This paper shows that prices may be sticky when buyers must search to determine the current market price and there is uncertainty about the expected duration of cost changes. Specifically, during periods when costs, and hence prices are high, low valuation consumers optimally stop searching and consequently are uninformed about price changes. Then, when costs go down, sellers must advertise to inform those consumers about price cuts. If advertising is costly, relative to single period profit, advertising is profitable only if the cost cut is likely to persist, but not if it is likely to be short lived. Thus, if sellers are initially uncertain about the expected longevity of a cost cut, they might adopt a 'watch and wait' strategy, delaying price reductions until better information becomes available. Importantly, it is shown that the same logic does not apply to cost increases. Thus the model is consistent with asymmetric price rigidity (e.g., Peltzman (2000)).