Most conventional 3D time-lapse (or 4D) acquisitions are ocean-bottom cable (OBC) or ocean-bottom node (OBN) surveys, as these surveys are relatively easy to replicate compared to towed-streamer surveys. To attain high degrees of repeatability and survey replicability, dense periodic sampling has become the norm for 4D surveys and renders this technology expensive. Conventional towed-streamer acquisitions suffer from limited illumination of the subsurface due to narrow azimuth. Although, acquisition techniques such as multiazimuth, wide-azimuth, rich-azimuth acquisition, etc., have been developed to illuminate the subsurface from all possible angles, these techniques can be prohibitively expensive for densely sampled surveys. This leads to uneven sampling — i.e., dense receiver and coarse source sampling or vice versa — to make these acquisitions more affordable. Motivated by the design principles of compressive sensing (CS), we perform a numerical study in which we acquire economic, randomly subsampled (or compressive), and simultaneous towed-streamer time-lapse data without the need of replicating surveys. We recover densely sampled time-lapse data on one and the same periodic grid by using a joint-recovery model that exploits shared information among different time-lapse recordings, coupled with a computationally inexpensive and scalable rank-minimization technique. The acquisition is low cost since we have subsampled measurements (about 70% subsampled) simulated with a simultaneous long-offset acquisition configuration of two source vessels traveling across a survey area at random azimuths. We analyze the performance of our proposed compressive acquisition and subsequent recovery strategy by conducting a synthetic at-scale seismic experiment on a 3D time-lapse model containing geologic features such as channel systems, dipping and faulted beds, unconformities, and a gas cloud. Our findings indicate that the insistence on replicability between surveys and the need for OBC/OBN 4D surveys can, perhaps, be relaxed. Moreover, this is a natural next step beyond the successful CS acquisition examples discussed in this special section.