Behavioral biologists have long been fascinated with the diversity of animal signals produced in the contexts of courtship and same-sex competition. In these contexts many lizards engage in conspicuous bobbing displays, and numerous studies have been devoted to describing these displays. Traditionally, bobbing displays are partitioned into units whose durations (and sometimes head amplitudes) are measured. Recently, Macedonia et al. (2019) introduced use of the Discrete Fourier Transform (DFT) as an alternative to unit-based variables for characterizing species-specific traits in display structure of Galápagos Lava Lizards (Microlophus spp.). The relative success of the two methods was not compared directly, however, because the homology of display units among species was uncertain. Here we overcome this problem using the “grahami series” of Anolis lizards—a monophyletic radiation of seven species on Jamaica and Grand Cayman. Our study had three primary goals. Our first goal was to discover whether DFT-based measures, unit-based measures, or their combination provided the best means to capture taxon-specific distinctiveness in display structure. To this end, we quantified bobbing displays and used nested analyses of variance (ANOVAs) to determine if particular variables were reliably superior at differentiating populations within a species. We then used principal components analysis to reduce the number of measurement variables, and entered the components into discriminant function analyses to determine which approach best discriminated among taxa. Results showed that no one type of measurement, or measurement combination, emerged as being consistently better at discriminating taxa across comparisons. Our second goal was to test a hypothesis that arose from our findings in Galápagos Lava Lizards—that the DFT may decrease in effectiveness as bobbing display structure increases in complexity. For this test we used four simple and compound display types from the species Anolis reconditus. Results of discriminant function analyses provided mixed support for the hypothesis, and we suggest that a definitive test of DFT performance and display complexity should utilize synthetic displays in which attributes of display structure are varied systematically. Last, we show how bobbing display structure maps onto alternative DNA-based phylogenies of the grahami series anoles. Whereas some species produced derived display types unanticipated from displays of more basal species in this adaptive radiation, others exhibited features that linked them to a particular population of a species in their clade.