Signal modeling techniques ranging from basis expansions to parametric approaches have been applied to audio signal processing. Motivated by the fundamental limitations of basis expansions for representing arbitrary signal features and providing means for signal modifications, we consider decompositions in terms of functions that are both signal-adaptive and parametric in nature. Granular synthesis and sinusoidal modeling can be viewed in this light; we interpret these approaches as signal-adaptive expansions in terms of time-frequency atoms that are highly correlated to the fundamental signal structures. This leads naturally to a discussion of the matching pursuit algorithm for deriving decompositions using over complete dictionaries of time-frequency atoms; specifically, we compare expansions using Gabor atoms and damped sinusoids. Such decompositions identify important signal features and provide parametric representations that are useful for signal coding and analysis-modification-synthesis.