ABSTRACT We present strong-lensing analyses of three galaxy clusters, RX J2129.4 + 0009 (z = 0.235), MS 0451.6 − 0305 (z = 0.55), and MACS J2129.4 − 0741 (z = 0.589), using the powerful combination of Hubble Space Telescope (HST) multiband observations, and Multi-Unit Spectroscopic Explorer (MUSE) spectroscopy. In RX J2129, we newly spectroscopically confirm 15 cluster members. Our resulting mass model uses 8 multiple image systems as we include a galaxy–galaxy lensing system north-east of the cluster, and is composed of 71 haloes including one dark matter cluster-scale halo and two galaxy-scale haloes optimized individually. For MS 0451, we report the spectroscopic identification of two new systems of multiple images in the northern region and 112 cluster members. Our mass model uses 16 multiple image systems and 146 haloes, including 2 large-scale haloes and 7 galaxy-scale haloes independently optimized. For MACS J2129, we report the spectroscopic identification of one new multiple image system at z = 4.41, and newly measure spectroscopic redshifts for four cluster members. Our mass model uses 14 multiple image systems, and is composed of 151 haloes, including 2 large-scale haloes and 4 galaxy-scale haloes independently optimized. Our best models have rms of 0.29, 0.6, 0.74 arcsec in the image plane for RX J2129, MS 0451, and MACS J2129, respectively. This analysis presents a detailed comparison with the existing literature showing excellent agreements, and discuss specific studies of lensed galaxies, e.g. a group of submillimetre galaxies at z = 2.9 in MS 0451, and a bright z = 2.1472 red singly imaged galaxy in MACS J2129.