One paradigm of Monte Carlo Tree Search (MCTS) improvements is to build and use state and/or action abstractions during the tree search. Non-exact abstractions, however, introduce an approximation error making convergence to the optimal action in the abstract space impossible. Hence, as proposed as a component of Elastic Monte Carlo Tree Search by Xu et al., abstraction algorithms should eventually drop the abstraction. In this paper, we propose two novel abstraction dropping schemes, namely OGA-IAAD and OGA-CAD which can yield clear performance improvements whilst being safe in the sense that the dropping never causes any notable performance degradations contrary to Xu's dropping method. OGA-IAAD is designed for time critical settings while OGA-CAD is designed to improve the MCTS performance with the same number of iterations.