Reliable calculations in Lattice QCD must confront excited-state contamination and statistical precision, where attempts to reduce excited-state effects are often handled with various "smearing" algorithms. Distillation, a particularly powerful form of smearing, has seen extensive use in spectroscopy calculations, yet, until now, has not seen use in calculations of hadronic structure. We find that distillation, and an extended basis of distilled interpolators facilitated by the variational method, applied to calculations of the scalar, axial and tensor isovector charges of the nucleon, lead to a dramatic reduction in statistical uncertainty and excited-state contamination when compared to conventional methods, thereby making a strong case for distillation in future, more elaborate, structure calculations.