The design of service policies whose aim is to minimize a linear combi
nation of average queue lengths, while keeping their variances below g
iven bounds, is considered in the context of a single-server system wi
th two job types. A family of readily implementable threshold policies
which can be used for this purpose is analysed in the steady state. T
he performance of these policies, as well as their ability to satisfy
constraints, is examined numerically and is compared to that of anothe
r simple family.