Precise timing of spikes between different neurons has been found to convey reliable information beyond the spike count. In contrast, the role of small and variable spiking delays, as reported, for example, in the visual cortex, remains largely unclear. This issue becomes particularly important considering the high speed of neuronal information processing, which is assumed to be based on only a few milliseconds within each processing step. We investigate the role of small and variable spiking delays with a parsimonious stochastic spiking model that is strongly motivated by experimental observations. The model contains only two parameters for the response of a neuron to one stimulus, describing directly the rate and the delay, or phase. Within the theoretical model, we specifically investigate two quantities, the probability of correct stimulus detection and the probability of correct change point detection, as a function of these parameters and within short periods of time. Optimal combinations of the two parameters across stimuli are derived that maximize these probabilities and enable comparison of pure rate, pure phase, and combined codes. In particular, the gain in correct detection probability when adding small and variable spiking delays to pure rate coding increases with the number of stimuli. More interesting, small and variable spiking delays can considerably improve the process of detecting changes in the stimulus, while also decreasing the probability of false alarms and thus increasing robustness and speed of change point detection. The results are compared to empirical spike train recordings of neurons in the visual cortex reported earlier in response to a number of visual stimuli. The results suggest that near-optimal combinations of rate and phase parameters may be implemented in the brain and that adding phase information could particularly increase the quality of change point detection in cases of highly similar stimuli.