This paper examines an important problem in smart grid energy scheduling; peaks in power demand are proportionally more expensive to generate and provision for. The issue is exacerbated in local microgrids that do not benefit from the aggregate smoothing experienced by large grids. Demand-side scheduling can reduce these peaks by taking advantage of the fact that there is often flexibility in job start times. We focus attention on the case where the jobs are non-preemptible, meaning once started, they run to completion. The associated optimization problem is called the Peak Demand Minimization problem and has been previously shown to be NP-hard. Our results include an optimal fixed-parameter tractable algorithm, a polynomial-time approximation algorithm, as well as an effective heuristic that can also be used in an online setting of the problem. Simulation results show these methods can reduce peak demand by up to 50% versus on-demand scheduling for household power jobs.