Source to receiver distances used in seismic data acquisition have been steadily increasing and it is now common to work with data acquired with more than 10 km of offset. Subbasalt exploration and seismic undershooting are just two applications in which long-offset reflections are sought. However, such reflections are often subjected to muting to suppress normal moveout (NMO) stretch artifacts, thus causing a loss of valuable information. To retrieve these portions of the recorded wavefield, we developed a nonstretch NMO correction based on wavelet estimation and on an iterative procedure of partial NMO correction and deconvolution. We evaluated this methodology using fourth-order traveltime curve approximations to increase the offset of usable reflections, but it can be adapted to traveltime curves of any order. Time- and space-variant wavelets, estimated by means of singular value decomposition along the sought traveltimes, were used to build the desired output for the deconvolution that aims at retrieving the original shape of the partially stretched wavelets. We tested our method on a synthetic gather presenting time and offset varying wavelets, on a real-marine line simulating an undershooting pattern and on true undershooting land-marine data. These examples demonstrated that our new algorithm effectively limits the stretching associated with the NMO correction and enables the recovery of those portions of the stacked sections that are typically lost from muting in the standard NMO correction.