Pre-print, Working paper: A memoryless agent can acquire arbitrarily many signals. After each signal observation, she either terminates and chooses an action, or she discards her observation and draws a new signal. By conditioning the probability of termination on the information collected, she controls the correlation between the payo_ state and her terminal action. We provide an optimality condition for the emerging stochastic choice. The condition highlights the bene_ts of selective memory applied to the extracted signals. Implications|obtained in a simple class of binary problems| include (i) confirmation bias, (ii) speed-accuracy complementarity, (iii) overweighting of rare events, and (iv) salience effect.