Continuous GPS time series from three of four recently measured, large subduction earthquakes document triggered rapid postseismic fault creep, representing an additional moment release upward of 25% over the weeks following their main shocks. Data from two Mw = 8.0 and Mw = 8.4 events constrain the postseismic centroids to lie down dip from the lower limit of coseismic faulting, and show that afterslip along the primary coseismic asperities is significantly less important than triggered deep creep. Time series for another Mw = 7.7 event show 30% postseismic energy release, but here we cannot differentiate between afterslip and triggered deeper creep. A fourth Mw = 8.1 event, which occurred in the broad Chilean seismogenic zone, shows no postseismic deformation, despite coseismic offsets in excess of 1 m. For the three events which are followed by postseismic deformation, stress transferred to the inferred centroids (at 34, 60, and 36 km depths) by their respective main shock asperities increased reverse shear stress by 0.5, 0.8, and 0.2 bar with a comparatively small decrease in normal stress (0.01 bar), constraining the Coulomb stress increase required to force slip along the metastable plate interface. Deep triggered slip of this nature is invisible without continuous geodesy but on the basis of these earthquakes would appear to constitute an important mode of strain release from beneath the seismogenic zones of convergent margins. These events, captured by some of the first permanent GPS networks, show that deep moment release is often modulated by seismogenic rupture updip and underscore the need for continuous geodesy to fully quantify the spectrum of moment release in great earthquakes.