Inspired by different conceptualizations of temporal neural coding schemes, there has been recent interest in the search for signs of precisely synchronized neural activity in the cortex. One method developed for this task is unitary-event analysis. This method tests multiple single-neuron recordings for short epochs with significantly more coincident spikes than expected from independent neurons. We reformulated the statistical test underlying this method using a coincidence count distribution based on empirical spike counts rather than on estimated spike probabilities. In the case of two neurons, the requirement of stationary firing rates, originally imposed on both neurons, can be relaxed; only the rate of one neuron needs to be stationary, while the other may follow an arbitrary time course. By analytical calculations of the test power curves of the original and the revised method, we demonstrate that the test power can be increased by a factor of two or more in physiologically realistic regimes. In addition, we analyze the effective significance levels of both methods for neural firing rates ranging between 0.2 Hz and 30 Hz.