Associated with Pacific-Australia plate convergence, the Lau Basin -- Havre Trough is an active back-arc basin that has been opened since ~5.5 Ma by rifting and southward propagating oceanic spreading. Current back-arc opening rates decrease from 159 mm yr-1 in the northern Lau Basin to 15 mm y-1 in the southern Havre Trough. Major tectonic changes occur at the transition between Havre Trough rifting and full oceanic spreading of the Eastern Lau Spreading Center (ELSC), where the oblique-to-trench, westward subducting Louisville Seamount Chain (LSC) sweeps southwards along the Tonga trench. New swath bathymetry, seismic reflection data, and limited rock sampling in this area constrain a tectonic and kinematic back-arc model that incorporates the effects of LSC subduction. The ELSC, which extends southward to 24¿55'S, forms a deep rift valley propagating southward through older, rifted arc basement. Present-day seismicity and fresh and fractured pillow lavas at 23¿42'S are consistent with rift valley neovolcanism. Conversely, the northern Havre Trough has low seismicity and rifted volcanic basement ridges trending 25--45¿ oblique to the basin axis consistent with low levels of extensional tectonism and volcanism. This latter structural fabric is interpreted as an early stage of rifting that is now locked due to compression on the arc exerted by LSC subduction, while in the Lau Basin such effects have passed as the LSC swept along the Tonga Trench. It is proposed that the Lau-Havre back-arc opening is controlled by tectonic constraints exerted at the limits of the system by the LSC subduction, which determines the southward migration of the Tonga Arc pole of rotation and associated Lau Basin opening. A discrete three-stage back-arc opening evolution is proposed, comprising: (1) an initial phase of back-arc rifting along the whole length of the plate boundary, beginning at ~6--5 Ma; (2) a subsequent phase, mostly present in the southern part of the back-arc domain and still active in the Havre Trough, of transpression and transtension, starting at ~4 Ma in the north, as the LSC starts to subduct and sweeps southward along the Tonga trench; and (3) a renewed opening phase in the northern segment of the back-arc domain, with rifting and spreading, starting at ~3.5 Ma, as subduction of the LSC along the northern Tonga trench is progressively completed.