Abstract: In nature foragers must exploit resources that vary randomly in both the energy acquired per item (reward) and the time required to pursue, capture and process an item (delay). Furthermore, rewards and delays associated with particular resources may often covary significantly. An analytical model asks how variance-covariance levels for rewards and delays could influence choice of resources when lack of information or cognitive limitation implies that a consumer attempts to maximize its short-term rate of energy gain. Both greater expected reward and reduced expected delay clearly should enhance preference for a resource. The model predicts that increased delay variance and reduced reward-delay covariance should increase a forager's preference for a resource. A forager should be risk-averse towards reward variance when the reward-delay covariance is positive, but should become risk-prone towards reward variance when the reward-delay covariance is negative.