An exact Lagrangian in a cotangent bundle that coincides with a cotangent fiber outside a compact set, and is disjoint from at least one cotangent fiber is called a nearby Lagrangian fiber. I will explain joint work in preparation with Yash Deshmukh and Alex Pieloch, showing that any nearby Lagrangian fiber in T*CP^2 or T*(S^{n-k} x R^k) is smoothly isotopic to a cotangent fiber rel boundary in the complement of the missed fiber. These results follows from a more general homotopy rigidity result for exact Lagrangian fillings of unknots in subcritical Weinstein manifolds.