In order to efficiently learn a dynamics model for a task in a new environment, one can adapt a model learned in a similar source environment. However, existing adaptation methods can fail when the target dataset contains transitions where the dynamics are very different from the source environment. For example, the source environment dynamics could be of a rope manipulated in free-space, whereas the target dynamics could involve collisions and deformation on obstacles. Our key insight is to improve data efficiency by focusing model adaptation on only the regions where the source and target dynamics are similar. In the rope example, adapting the free-space dynamics requires significantly fewer data than adapting the free-space dynamics while also learning collision dynamics. We propose a new method for adaptation that is effective in adapting to regions of similar dynamics. Additionally, we combine this adaptation method with prior work on planning with unreliable dynamics to make a method for data-efficient online adaptation, called FOCUS. We first demonstrate that the proposed adaptation method achieves statistically significantly lower prediction error in regions of similar dynamics on simulated rope manipulation and plant watering tasks. We then show on a bimanual rope manipulation task that FOCUS achieves data-efficient online learning, in simulation and in the real world.