An agent acquires information dynamically until her belief about a binary state reaches an upper or lower threshold. She can choose any signal process subject to a constraint on the rate of entropy reduction. Strategies are ordered by “time risk”—the dispersion of the distribution of threshold-hitting times. We construct a strategy maximizing time risk (Greedy Exploitation) and one minimizing it (Pure Accumulation). Under either, beliefs follow a compensated Poisson process. In the former, beliefs jump to the threshold closer in Bregman divergence. In the latter, beliefs jump to the unique point with the same entropy as the current belief.