Most of underwater wireless sensor applications need reliable data transfer timely and efficiently. Because radio waves do not travel well through good electrical conductors like saltwater, underwater distributed systems use acoustic waves to communicate data. However, energy conservation is a major challenge in underwater acoustic-based systems/networks. Different methods are developed to enhance energy efficiency in these networks. In this paper, we improve energy efficiency of the networks by enhancing routing scheme. The enhancement is done by defining some constraints on traditional packet flooding. A strategy based on physical constraints has been introduced in our previous work for creating an indirect 1-D random mechanism to remove additional nodes from routing process and save energy. Now here, a better mechanism in terms of simplicity, scalability and efficiency is introduced to improve energy consumption. The approach is to use an intelligent 3-D random node removal mechanism considering traffic status of the network. Simulation results show that the proposed approach significantly improves energy efficiency of the underwater acoustic wireless sensor networks.