We revisit the longstanding view that pulsar radio spectra, which describe how radio brightness varies with frequency, are predominantly simple power laws. Using calibrated flux-density measurements for 897 pulsars, we compare six spectral models through Bayesian inference and frequentist methods. Reconstructing an earlier analysis reveals how its model-selection rule could exclude complex models for sparsely sampled spectra, contributing to the reported dominance of simple power laws. This comparison helps distinguish the effects of statistical methodology from the spectral properties of the pulsars themselves.
Broken power laws are the most common classification in our Bayesian analysis, accounting for 60.1% of the full sample, while simple power laws describe 13.5%. Among the 884 categorized pulsars, 68.8% decisively favor curved or broken models over a simple power law. We also identify 74 confident gigahertz-peaked-spectrum candidates, with peaks between 0.6 and 2.0 GHz, and find that spectral curvature is common among millisecond pulsars. Together, these results establish the prevalence of complex spectra in the analyzed sample and provide a catalog of spectral classifications for studying pulsar emission and absorption processes.