We make use of twisted boundary conditions for off-shell, Rome-Southampton renormalization. This allows us to define vertex functions at a fixed physical momentum that need not be a Fourier mode. This definition includes choosing a fixed orientation with respect to the lattice axes; only then do lattice artifacts, which include breaking effects, have a valid expansion in powers of the lattice spacing, . The use of nonexceptional momenta has been found to greatly reduce the dependence of the vertex functions on both mass and momentum, . Excellent statistical precision is afforded by plane-wave sources. Together this enables both a theoretically well-founded and statistically clean continuum limit. Thereafter all dependence can be identified with the anomalous running of the operator. We present initial results and develop a practical scheme for step-scaling with off-shell renormalization. The size of the steps is continuous rather than discrete, allowing arbitrarily small steps and the scheme is easy to implement for general operators.