Graphics processing units (GPUs) are extensively used as accelerators across multiple application domains, ranging from general purpose applications to neural networks, and cryptocurrency mining. The initial utilization paradigm for GPUs was one application accessing all the resources of the GPU. In recent years, time sharing is broadly used among applications of a GPU, nevertheless, spatial sharing is not fully explored. When concurrent applications share the computational resources of a GPU, performance can be improved by eliminating idle resources. Additionally, the incorporation of GPUs in embedded and mobile devices increases the demand for power efficient computation due to battery limitations. In this article, we present an allocation methodology for streaming multiprocessors (SMs). The presented methodology works for two concurrent applications on a GPU and determines an allocation scheme that will provide power efficient application execution, combined with improved GPU performance. Experimental results show that the developed methodology yields higher throughput while achieving improved power efficiency, compared to other SM power-aware and performance-aware policies. If the presented methodology is adopted, it will lead to higher performance of applications that are concurrently executing on a GPU. This will lead to a faster and more efficient acceleration of execution, even for devices with restrained energy sources.