Real-time search is a well known approach to solving search problems under tight time constraints. Recently, it has been shown that LSS-LRTA*, a well-known real-time search algorithm, can be improved when search is actively guided away of depressions. In this paper we investigate whether or not RTAA* can be improved in the same manner. We propose aRTAA* and daRTAA*, two algorithms based on RTAA* that avoid heuristic depressions. Both algorithms outperform RTAA* on standard path-finding tasks, obtaining better quality solutions when the same time deadline is imposed on the duration of the planning episode. We prove, in addition, that both algorithms have good theoretical properties. Copyright © 2011, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.