Energy consumption of an application has gained the same importance as execution time in current HPC systems, primarily due to the massive energy consumption of these systems and consequently substantial energy bills. This fact forced software developers as well as hardware vendors to put an extensive focus on energy consumption. This focus becomes even more crucial in power constrained systems, where the amount of power dedicated to applications is limited. In such systems, finding the optimal balance between execution time and energy consumption has a significant impact on utilizing these systems efficiently. A programming model is an essential layer where optimizations can be applied to find the optimal balance.OpenMP is a standard programming model for intra-node parallelism. In this paper, we give a detailed analysis of how to optimize the execution time and energy consumption of an OpenMP application using the OpenMP runtime environment at different power levels. We studied twenty-eight OpenMP parallel regions from five NAS Parallel Benchmark (NPB) applications. Based on the study, we show that for a given power level, a suitable selection of OpenMP runtime parameters can improve the execution time and energy consumption of a parallel region up to 67% and 72%, respectively. We also show that these fine-grained improvements resulted in up to 26% of execution time and 38% of energy consumption improvement for a given OpenMP application. We finally observed that optimizing the energy consumption behavior alone across all power levels regardless of execution time behavior can lead to an additional energy consumption improvement of up to 55%. However, this improvement comes at the expense of execution time.