Spurious real solutions kS >= 1 Å-1 of the bulk k∙p Hamiltonian for semiconductors can lead to spurious bands and nonnormalizable wave functions in the envelope function approximation (EFA). Since physical observables cannot depend on layer width variations on the scale of 1 Å—less than a typical interface width or the precision of defining an interface—we form coherent superpositions of spurious real solutions that satisfy boundary conditions with interface boundaries varying on the scale of kS-1. The superposition leads to a total destructive interference, which demonstrates that real spurious solutions do not contribute to the envelope function away from interfaces. In the interfacial region, we show that real spurious solutions should be replaced with evanescent solutions that decay within kS-1. The present technique is demonstrated in a model case and in a superlattice calculation using the 8 × 8 EFA.