Conformational changes that occur upon ligand binding may be too slow to observe on the time scales routinely accessible using molecular dynamics simulations. The adaptive integration method (AIM) leverages the notion that when a ligand is either fully coupled or decoupled, according to A, barrier heights may change, making some conformational transitions more accessible at certain A values. AIM adaptively changes the value of A in a single simulation so that conformations sampled at one value of A seed the conformational space sampled at another A value. Adapting the value of A throughout a simulation, however, does not resolve issues in sampling when barriers remain high regardless of the A value. In this work, we introduce a new method, called Accelerated AIM (AcclAIM), in which the potential energy function is flattened at intermediate values of A, promoting the exploration of conformational space as the ligand is decoupled from its receptor. We show, with both a simple model system (Bromocyclohexane) and the more complex biomolecule Thrombin, that AcclAIM is a promising approach to overcome high barriers in the calculation of free energies, without the need for any statistical reweighting or additional processors.