A fundamental concern in real-time planning is the presence of dead ends in the state space, from which no goal is reachable. Recently, the SafeRTS algorithm was proposed for searching in such spaces. SafeRTS exploits a user-provided predicate to identify safe states, from which a goal is likely reachable, and attempts to maintain a backup plan for reaching such a state at all times. In this paper, we study the SafeRTS approach, identify certain properties of its behavior, and design an improved framework for safe real-time search. We prove that the new approach performs at least as well as SafeRTS and present experimental results showing that its promise is fulfilled in practice.