We present a diagnostic glacier flowline model parameterized and constrained by new velocity data from ice-surface GPS installations and speckle tracking of TerraSAR-X satellite images, newly acquired airborne-radar data, and continental gridded datasets of topography and geothermal heat flux, in order to better understand two outlet glaciers of the East Antarctic ice sheet. Our observational data are employed as primary inputs to a modelling procedure that first calculates the basal thermal regime of each glacier, then iterates the basal sliding coefficient and deformation rate parameter until the fit of simulated to observed surface velocities is optimized. We find that the two glaciers have both frozen and thawed areas at their beds, facilitating partial sliding. Glacier flow arises from a balance between sliding and deformation that fluctuates along the length of each glacier, with the amount of sliding typically varying by up to two orders of magnitude but with deformation rates far more constant. Beardmore Glacier is warmer and faster-flowing than Skelton Glacier, but an up-glacier deepening bed at the grounding line, coupled with ice thicknesses close to flotation, lead us to infer a greater vulnerability of Skelton Glacier to grounding-line recession if affected by ocean-forced thinning and concomitant acceleration.