This study investigates the directional predictability of overnight periods for intraday returns of large Australian stocks. The intraday reactions to overnight developments are studied using cross-quantilograms, a new, flexible methodology that facilitates detailed insights into the quantile dependence between two time series. The results provide evidence for the existence of intraday reversals after overnight periods that carry very bad news, whereas the picture of the short-term reactions to very positive overnight returns is mixed. The observed rebounds concern extreme quantiles and occur with a short delay during the first part of the trading day. The study also shows that continuation and reversal effects are not mutually exclusive. The economic significance of the identified patterns is illustrated by analysing the performance of a simple contrarian strategy.