Satellite systems typically use physical and link layer reliability schemes to compensate the significant channel impairments, especially for the link between a satellite and a mobile end-user. These schemes have been introduced at the price of an increase in the end-to-end delay, high jitter or out-of-order packets. This is show to have a negative impact both on multimedia and best-effort traffic, decreasing the Quality of Experience (QoE) of users. In this paper, we propose to solve this issue by scheduling data transmission as a function of the channel condition. We first investigate existing scheduling mechanisms and analyze their performance for two kinds of traffic: VoIP and best-effort. In the case of VoIP traffic, the objective is to lower both latency and jitter, which are the most important metrics to achieve a consistent VoIP service. We select the best candidate among several schedulers and propose a novel algorithm specifically designed to carry VoIP over LEO constellations. We then investigate the performance of the scheduling policies on Internet-browsing traffic carried by TCP, where the goal is now the maximize the users' goodput, and select the best candidate in this case.