Black hole perturbation theory is typically studied on time surfaces that extend between the bifurcation sphere and spatial infinity. I will argue that–from a physical point of view–it is favorable to employ time surfaces that extend between the future event horizon and future null infinity. I will demonstrate how this new approach resolves problems related to the representation of quasinormal mode eigenfunctions, the construction of short-ranged potentials for curvature perturbations, and the numerical calculation of gravitational waveforms as measured by an idealized observer.