The Blankenbecler-Goldberger approximation to scattering amplitude (1962) is applied to the elastic e-H and e-He scattering. For small momentum transfers, q²<or approximately=1 (in units of a₀^-2), there is hardly any difference in d sigma /d Omega between the Glauber and the Blankenbecler-Goldberger predictions though the latter stays consistently below the Glauber prediction (1959). For larger momentum transfers, q²>>1, the difference becomes more marked with the Glauber prediction staying higher. However as d sigma /d Omega drops by three orders of magnitude at q² approximately=10 the Blankenbecler-Goldberger prediction for sigma _el will not be much different from that of the Glauber prediction.