The application of Sentinel-1 interferometry to ice velocity measurements has until recently been limited by the significant horizontal scene motion associated with ice flow, which causes phase discontinuities (and associated unwrapping problems) at burst boundaries in Terrain Observation by Progressive Scans (TOPS) interferograms. Coregistering with a multiyear averaged external velocity mosaic based on offset-tracking can account for the bulk of the ice motion, but residual discontinuities sometimes remain, for example, due to seasonal variations in the ice velocity, or due to error sources such as azimuth shifts caused by ionospheric propagation. The presented method extends the external velocity coregistration with a local, spatially varying, coregistration in the burst overlap regions. This is based on the extended spectral diversity principle, which can only be applied in the overlap regions, but offers superior accuracy and resolution compared with traditional coregistration methods. The method considerably reduces phase discontinuities at burst boundaries, and potential new phase discontinuities at the overlap region edges are suppressed by an azimuth tapering of the applied coregistration shifts. An example scene is presented, and the phase discontinuities before and after application of the method are evaluated. The method is seen to remove phase discontinuities, with no adverse effects.