High-security processes typically have to load confidential information, such as encryption keys or private data, into memory as part of their operation. In systems with a single shared memory, when high-security processes are switched out due to context switching, confidential information may remain in memory and be accessible to low-security processes. This paper considers this problem from the perspective of scheduling. A formal model supporting preemption is introduced that allows: reasoning about leakage between high-and low-security processes, and producing information-leakage aware schedulers. Several information-leakage aware heuristics are presented in the form of compositional pre-and postprocessors as part of a more general scheduling approach. The effectiveness of such heuristics is evaluated experimentally, showing them to achieve significantly better schedulability than the state of the art.