Recently, dopamine (DA) neurons of the substantia nigra pars compacta (SNc) were found to exhibit sustained responses related to reward uncertainty, in addition to the phasic responses related to reward-prediction errors (RPEs). Thus, cue-dependent anticipations of the timing, magnitude, and uncertainty of rewards are learned and reflected in components of DA signals. Here we simulate a local circuit model to show how learned uncertainty responses are generated, along with phasic RPE responses, on single trials. Both types of simulated DA responses exhibit the empirically observed dependencies on conditional probability, expected value of reward, and time since onset of the reward-predicting cue. The model's three major pathways compute expected values of cues, timed predictions of reward magnitudes, and uncertainties associated with these predictions. The first two pathways' computations refine those modeled by Brown et al. (1999). The third, newly modeled, pathway involves medium spiny projection neurons (MSPNs) of the striatal matrix, whose axons corelease GABA and substance P, both at synapses with GABAergic neurons in the substantia nigra pars reticulata (SNr) and with distal dendrites (in SNr) of DA neurons whose somas are located in ventral SNc. Corelease enables efficient computation of uncertainty responses that are a nonmonotonic function of the conditional probability of reward, and variability in striatal cholinergic transmission can explain observed individual differences in the amplitudes of uncertainty responses. The involvement of matricial MSPNs and cholinergic transmission within the striatum implies a relation between uncertainty in cue-reward contingencies and action-selection functions of the basal ganglia.