An iterative numerical integration procedure has been developed to correct both beta spectra and differential beta‐gamma directional correlations for the effects of finite instrument energy resolution including the effect of backscattering from a scintillation detector.The method has been tested and found to reproduce the true spectral shape in the cases of Re186, Au198, Tl204, and to allow separation of composite beta spectra as in the case of W187. Application of the method is limited to maximum beta energies exceeding 200 kev.