Giant planet formation by gravitational disc instabilities has become theoretically and observationally acceptable at large distances, but remains theoretically contentious at distances inside about 20 au. Several new three-dimensional hydrodynamics models are presented, where radiative transfer is handled in the flux-limited diffusion approximation from the very start of the model, rather than being employed only after clumps have begun to form. The three models show that the use of the flux limiter has little appreciable effect on the early evolution of a disc instability, in agreement with the conclusions of the previous models, which studied later phases. In addition, two new models are presented where the central protostar is either held fixed or is allowed to wobble in such a manner as to preserve the centre of mass of the star–disc system. While spiral arms and clumps form in both models, the wobbling protostar model appears to be better able to form self-gravitating clumps that could contract to form gas giant protoplanets. Combined with previous results, the new models imply that disc instability should be able to form self-gravitating clumps inside, as well as outside, 20 au in suitably massive and cool protoplanetary discs.