We develop an automated technique for fitting the spectral components of solar microwave spike bursts, which are characterized by narrowband spectral features. The algorithm is especially useful for periods when the spikes occur in densely packed clusters, where the algorithm is capable of decomposing overlapping spike structures into individual spectral components. To test the performance and applicability limits of this data reduction tool, we perform comprehensive modeling of spike clusters characterized by various typical bandwidths, spike densities, and amplitude distributions. We find that, for a wide range of favorable combinations of input parameters, the algorithm is able to recover the characteristic features of the modeled distributions within reasonable confidence intervals. Having model-tested the algorithm against spike overlap, broadband spectral background, noise contamination, and possible malfunction of some spectral channels, we apply the technique to a spike cluster recorded by the Chinese Purple Mountain Observatory (PMO) spectrometer, operating above 4.5 GHz. We study the variation of the spike distribution parameters, such as amplitude, bandwidth, and related derived physical parameters, as a function of time. The method can be further applied to observations from other instruments and to other types of fine structures.