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Compact binaries may be formed dynamically in globular clusters, with large (close to unity) orbital eccentricity and emitting gravitational waves within the detection band of ground based detectors. The gravitational waves from such sources resemble more a discrete set of bursts than the continuous signal of their quasi-circular counterparts. I here discuss the construction of new analytic waveforms for such systems, which rely on treating the problem as a perturbation of a parabolic fly-by. I will discuss the results of parameter estimation with these waveforms for binary black holes, and the inclusion of tidal effects for binary neutron stars.