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Abstract While solar-like oscillations in red giants have been observed at massive scales by the Kepler mission, few features of these oscillation mode frequencies, other than their global properties, have been exploited for stellar characterization. The signatures of acoustic glitches in mode frequencies have been used for studying main-sequence stars, but the validity of applying such techniques to evolved red giants, particularly pertaining to the inclusion of nonradial modes, has been less well examined. Making use of new theoretical developments, we characterize glitches using theπmodes associated with red giant stellar models, and use our procedure to examine for the first time how the properties of the Heiiacoustic glitch—specifically its amplitude and associated acoustic depth—vary over the course of evolution up the red giant branch, and with respect to other fundamental stellar properties. We find that the acoustic depths of these glitches, in conjunction with other spectroscopic information, discriminate between red giants in the first-ascent and core-helium-burning phases. We critically reexamine previous attempts to constrain acoustic glitches from nonradial (in particular dipole) modes in red giants. Finally, we apply our fitting procedure to Kepler data, to evaluate its robustness to noise and other observational systematics.