We present a family of policies that, integrated within a runtime task scheduler (Nanox), pursue the goal of improving the energy efficiency of task-parallel executions with no intervention from the programmer. The proposed policies tackle the problem by modifying the core operating frequency via DVFS mechanisms, or by enabling/disabling the mapping of tasks to specific cores at selected execution points, depending on the internal status of the scheduler. Experimental results on an asymmetric SoC (Exynos 5422) and for a specific operation (Cholesky factorization) reveal gains up to 29% in terms of energy efficiency and considerable reductions in average power.