Two related formulations are proposed for target-oriented joint least-squares migration/inversion of time-lapse seismic data sets. Time-lapse seismic images can be degraded when reservoir overburden is complex or when acquisition geometries significantly differ, because the migration operator does not compensate for the resulting amplitude and phase distortions. Under these circumstances, time-lapse amplitudes are poor indicators of production-related changes in reservoir properties. To correct for such image degradation, time-lapse imaging is posed as joint inverse problems that utilize concatenations of target-oriented approximations to the linear least-squares imaging Hessian. In both formulations, spatial and temporal constraints ensure inversion stability and geologically consistent time-lapse images. Using two numerical time-lapse data sets, we confirmed that these formulations can attenuate illumination artifacts caused by complex overburden or geometry differences, and that they yield better-quality images than obtainable with migration.