Partially observable planning is one of the most general and useful models for dealing with complex problems. In recent years there have been significant progress on the development of planners for deterministic models that offer strong theoretical guarantees over certain subclasses of tasks. These guarantees however are difficult to establish as they often involve reasoning about features that are specific to the planner and subclass of tasks. In this paper we develop a formal framework for reasoning about online planning over deterministic tasks, identify a set of general conditions that are sufficient to guarantee completeness, and obtain novel and simple planners that are complete over non-trivial and interesting classes of tasks. Building on top state-of-the-art online planners, we implement some of our ideas and make a comparison with a state-of-the-art online planner.