Iceberg calving is a dominant mass loss mechanism for Antarctic ice shelves, second only to basal melting. An important known process involved in calving is the initiation and propagation of through-penetrating fractures called rifts; however, the mechanisms controlling rift propagation remain poorly understood. To investigate the mechanics of ice-shelf rifting, we analyzed seismicity associated with a propagating rift tip on the Amery Ice Shelf, using data collected during the Austral summers of 2004-2007. We investigated seismicity associated with fracture propagation using a suite of passive seismological techniques including icequake locations, back projection, and moment tensor inversion. We confirm previous results that show that seismicity is characterized by periods of relative quiescence punctuated by swarms of intense seismicity of one to three hours. However, even during periods of quiescence, we find significant seismic deformation around the rift tip. Moment tensors, calculated for a subset of the largest icequakes (M_W > -2.0) located near the rift tip, show steeply dipping fault planes, horizontal or shallowly plunging stress orientations, and often have a significant volumetric component. They also reveal that much of the observed seismicity is limited to the upper 50 m of the ice shelf. This suggests a complex system of deformation that involves the propagating rift, the region behind the rift tip, and a system of rift-transverse crevasses. Small-scale variations in the mechanical structure of the ice shelf, especially rift-transverse crevasses and accreted marine ice, play an important role in modulating the rate and location of seismicity associated with propagating ice shelf rifts.