Several pairs of normal mode multiplets sensitive to long-wavelength mantle structure are potential coupling partners. Geometric selection rules render such coupling the only means by which normal modes sample odd-degree mantle structure. That overtone coupling can be strong and can significantly impact normal mode spectra is illustrated using synthetic seismograms for a realistic earth model. These observations motivate the generalization of normal mode spectral fitting to permit simultaneous estimation of even- and odd-degree structural constraints. When generalized spectral fitting is applied to a data set of approximately 150 high signal-to-noise vertical records, dominated by data from the Northern Bolivian event (6/9/1994), it is found to reduce misfits appreciably for coupled multiplets 1S5–2S4 and 2S5–1S6, to yield odd-degree constraints generally consistent with recent mantle models, and to improve agreement between estimated and predicted even-degree constraints.