Spike counts (SC) or, spike rate and first spike latency (FSL), are both used to evaluate the responses of neurons to amplitudes and frequencies of acoustic stimuli. However, it is unclear which one is more suitable as a parameter for evaluating the responses of neurons to acoustic amplitudes and frequencies, since systematic comparisons between SC and FSL tuned to different amplitudes and frequencies, are scarce. This study systematically compared the precision and stability (i.e., the resolution and the coefficient variation, CV) of SC- and FSL-function as frequencies and amplitudes in the inferior colliculus of mice. The results showed that: (1) the SC-amplitude functions were of diverse shape (monotonic, nonmonotonic and saturated) whereas the FSL-amplitude functions were in close registration, in which FSL decreased with the increase of amplitude and no paradoxical (an increase in FSL with increasing amplitude) or constant (an independence of FSL on amplitude) neuron was observed; (2) the discriminability (resolution) of differences in amplitude and frequency based on FSL are higher than those based on SC; (3) the CVs of FSL for low amplitude stimuli were smaller than those of SC; (4) the fraction of neurons for which BF=CF (within +/-500Hz) obtained from FSL was higher than that from SC at any amplitude of sound. Therefore, SC and FSL may vary, independent from each other and represent different parameters of an acoustic stimulus, but FSL with its precision and stability appears to be a better parameter than SC in evaluation of the response of a neuron to frequency and amplitude in mouse inferior colliculus.