Traditional multiperiod models of asset markets assume that traders take the information filtration as given. This paper explores the effect of endogenizing the arrival of information on the dynamic completeness of markets. It is shown that if an agent is allowed to release information (at a sufficiently small cost) which prevents traders from dynamically completing the market, she might choose to do so. Furthermore we show that in economies with enough heterogeneity, it is always possible to find an agent who would choose to release information. Thus, with endogenous timing of information, markets are unlikely to be dynamically complete