Conventional moveout analysis stretches and squeezes traces to increase the coherence of reflected amplitudes in prestack seismic gathers. Higher order residual moveouts require increasingly difficult scans of semblances with extra dimensions or picking from correlations with many local minima. Alternatively, we can model our data with an adaptive convolution that assumes consistent reflectivities at all offsets (or angles). Short, convolutional wavelets can adjust residual moveouts arbitrarily with offset, but slowly with time (or depth). A Gauss-Newton optimization easily inverts this transform by minimizing a least-squares objective function. With estimated and normalized wavelets, we deconvolved the original data to remove phase and spectral distortions that affected more than one reflection. By constraining how slowly wavelets adapt, we retained phase and amplitude changes distinctive to individual reflections. Deconvolution also avoided any explicit smoothing or mixing of amplitudes among traces. Estimated wavelets captured residual coherence and were easier to track visually than individually weak reflections. By adjusting the length and number of independent dynamic wavelets, we can adjust the resolution to the redundancy supported by the data.