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We present improved modelling of the redshift-space distortions of galaxy clustering that arise from peculiar velocities. We create mock galaxy catalogues in the framework of the halo model, using data from the Bolshoi project. These mock galaxy populations are inserted into the haloes with additional degrees of freedom that govern spatial and kinematical biases of the galaxy populations relative to the dark matter. We explore this generalised halo model with an MCMC algorithm, comparing the predictions to data from the Galaxy And Mass Assembly (GAMA) survey, and thus derive one of the first constraints on the detailed kinematic degrees of freedom for satellite galaxies within haloes. With this approach, the distortions of the redshift-space galaxy autocorrelations can be accounted for down to spatial separations close to 10 kpc, opening the prospect of improved RSD measurements of the perturbation growth rate by the inclusion of data from nonlinear scales.