In this paper we show that the adjoint formulation of the Stretch-Fold-Shear (SFS) fast dynamo model has smooth eigenfunctions at zero diffusivity. We thus compute fast dynamo action with smooth fields. We note that the adjoint problem is equivalent to use of a vector potential in reversed flow. We compare this behavior with analogous results for general pulsed-flow models. Some calculations using pulsed Beltrami waves are described.