Variable-depth streamer acquisition is now widely used, achieving a bandwidth of more than 6 octaves (2.5 to 200 Hz) and excellent lateral resolution and providing improved impedance and reservoir analysis. This acquisition and processing method is based on towing the streamer deep, using a variable-depth profile optimized to ensure receiver notch diversity at the imaging stage and a deghosting method that takes advantage of the notch diversity. For 4D processing of monitors now acquired with variable-depth cables and with a baseline consisting of a flat towed streamer, we must deal with two processing issues. First, raypaths of traces acquired at the same surface locations differ; second, receiver ghosts lead to different wavelets. A 4D coprocessing flow is introduced that codatums 4D vintages to a common datum early in the sequence. Furthermore, a new deghosting technique is applied to variable-depth and conventional data. This processing flow gives excellent repeatability with 4D noise of less than 10% on a zero-time repeatability test with North Sea data from 2013.