In this study, two approximate high-order maximum-entropy-based closures in velocity space are coupled to a 5-moment maximum-entropy closure in droplet size space to model the behaviour of polydisperse polykinetic sprays. The two approximations of the high-order 14-moment maximum-entropy closures in velocity space (14-moment in three space dimensions, 5-moment in one space dimension) considered here are an interpolative-based approach and a closure based on a bi-Gaussian approximation for the distribution function.