In the past few years, many researchers attempted to tackle the problem of decreasing energy consumption in cloud data centers. One of the widely adopted techniques for this purpose is dynamic Virtual Machine (VM) consolidation. Consolidation moves VMs between hosts to decrease energy consumption. However, it has a negative impact on performance leading to Service Level Agreement (SLA) violations. Accordingly, selecting which VM to migrate from one host to another is a challenging task since it can affect performance. Researchers came up with several solutions and policies for efficient VM selection. In this paper, we exploit the fact that many tasks and users may tolerate some performance degradation which means, the tasks running on the VMs can be of different priorities. Accordingly, we propose augmenting consolidation with the priority concept, where low priority tasks are always selected first for migration. Towards this goal, we modified the popular Minimum Migration Time VM selection algorithm using the priority concept. The efficiency of the proposed algorithm is confirmed through extensive simulations using CloudSim toolkit and a real workload. The results show that priority awareness has a positive impact on decreasing energy consumption as well as maximizing SLA obligation.