Kah et al. (2010) recently developed the Eulerian Multi-Size Moment model (EMSM) which tackles the modelling and the numerical aspects for the simulation of polydisperse multiphase flows of a gaseous flow field carrying a disperse liquid phase. Using a moment method, they proposed to reconstruct the number density function (NDF) by Entropy Maximisation , which leads to a unique and realizable NDF. This reconstruction is used to simulate the evaporation process, by an evaluation of the flux of droplet disappearance at zero size and an accurate description of the size shift induced by the evaporation as well as the transport in physical space. Although this method demonstrated its great potential for evaporating polydisperse flows, two issues remain to be addressed. First, the EMSM only considers one velocity for all droplets, thus decoupling size from velocity, which will be to restrictive for distributions with a large size spectrum. In most applications size-conditioned dynamics have to be accounted for. Second, the possibility to have separated dynamics for each size can lead to quasi-monodisperse distributions, which corresponds to a hard limiting case for the entropy maximization algorithm. So the behavior of the entropy maximization needs to be investigated, in order to be able to reproduce a larger subset of the moment space. The aim of this paper is thus twofold. First, the entropy maximization and its related algorithm are enhanced by using a more precise integration method in order to handle NDF close to the frontier of the moment space associated with an adaptive number of parameters to reconstruct the NDF accurately and efficiently, as well as tabulated initial guess to optimize the computational time. Then, a new model called CSVM (Coupled Size-Velocity Moments model) is proposed. Size-velocity correlations are addressed either in the evaporation and drag processes, or in the convective transport. To reach this goal, a reconstruction of the velocity for each size is proposed, using only one additional moment per dimension. This reconstruction is evaluated in evaporation-drag 0D cases, to assess its ability to reproduce both phenomena. To handle the convective transport, a new flux splitting scheme is proposed, based on the underlying kinetic description of the disperse phase. The full strategy is evaluated in 1D and 2D cases and shows the ability of the CSVM and its related algorithms to capture the full physics of polydisperse evaporating sprays with a minimal number of moments.