The proliferation of birdsong research into the neural mechanisms of vocal learning is indebted to the remarkable stereotypy of the zebra finch's song motif. Motifs are composed of several syllables, which birds learn to produce in a fixed order. But at a higher level of organization-the bout-zebra finch song is no longer stereotyped. Song bouts include several repetitions of the motif, which are often linked by a variable number of short "connector" vocalizations. In this conceptual methods paper, we show that combinatorial analysis alone yields an incomplete description of this bout-level structure. In contrast, studying birdsong as a time-varying analog signal can reveal patterns of flexibility in the rhythmic organization of song bouts. Visualizing large song-samples in sorted raster plots shows that motifs are strung together via two distinct categories of connections: tight or loose. Loose connections allow considerable timing variation across renditions. Even among co-tutored birds that acquired similar motifs, we observe strong individual variability in rhythms and temporal plasticity of song bouts. These findings suggest that vocal flexibility could potentially allow individuals to express a variety of behavioral states through their songs, even in species that sing only a single stereotyped motif.