Two great underthrusting earthquakes that occurred along the coast of Peru in 2001 and 2007 involve spatiotemporal slip distributions that differ from the predominantly unilateral or bilateral rupture expansion of many great events. Commonly used finite-source rupture model parameterizations, with specified rupture velocity and/or short duration of slip at each grid point applied to the seismic data for these two events, lead to incorrect slip-distributions or inaccurate estimation of rupture velocities as a result of intrinsic kinematic constraints imposed on the model slip distributions. Guided by large aperture array back projections of teleseismic broadband P-wave signals that image slip locations without imposing a priori kinematic constraints on the rupture process, we exploit the availability of large global broadband body and surface wave data sets to consider the effects of varying the kinematic constraints in teleseismic finite-source waveform inversions. By allowing longer than usual rupture durations at each point on the fault using a flexible subfault source-time function parameterization, we find that the anomalous attributes of the 2001 and 2007 Peru earthquake ruptures are readily recognized and accounted for by compound rupture models. The great 23 June 2001 (Mw 8.4 8.4) earthquake involved an initial modest-size event that appears to have triggered a much larger secondary event about 120 km away that developed an overall slip distribution with significant slip located back along the megathrust in the vicinity of the initial rupture. The great 15 August 2007 (Mw 8.0 8.0) earthquake was also a composite event, with a modest size initial rupture followed by a 60-sec delayed larger rupture that initiated ∼50–60 km away and spread up-dip and bilaterally. When back projections indicate greater rupture complexity than captured in a simple slip-pulse-type rupture model, one should allow for possible long-subfault slip-duration or composite triggered sequences, and not overly constrain the earthquake slip distribution.