Motion planning in dynamic environments consists of the generation of a collision-free trajectory from an initial to a goal state. When the environment contains uncertainty, preventing a perfect predictive model of its dynamics, a robot ends up only successfully executing a short part of the plan and then requires replanning, using the latest observed state of the environment. Each such replanning step is computationally expensive. Furthermore, we note that such sophisticated planning effort is unnecessary as the resulting plans are not likely to ever be fully executed, due to an unpredictable and changing environment. In this paper, we introduce the concept of Variable Level-Of-Detail (VLOD) planning, that is able to focus its search on obtaining accurate short-term results, while considering the far-future with a different level of detail, selectively ignoring the physical interactions with poorly predictable dynamic objects (e.g., other mobile bodies that are controlled by external entities). Unlike finite-horizon planning, which limits the maximum search depth, VLOD planning deals with local minima and generates full plans to the goal, while requiring much less computation than traditional planning. We contribute VLOD planning on a rich simulated physics-based planner and show results for varying LOD thresholds and replanning intervals.