The utility of an approximation method for dealing with low symmetry, confined systems using basis functions that do not satisfy the boundary conditions is demonstrated by applying it to the problem of off-axis hydrogenic impurities in cylindrical quantum well wires. Results of calculations of binding energies are presented as a function of the wire radius and the displacement of the impurity from the axis. A previously unexpected behaviour of the binding energy as the location of the impurity and the radius of the well are varied is displayed.