Abstract Higher-order corrections to small-angle Bhabha scattering are investigated. The use of this process as a high-precision luminosity measurement at LEP requires a careful discussion of corrections beyond the well-established order-α case. It is shown that an accuracy of 0.5% necessitates the consideration of leading log order-α2 corrections, including those of double bremsstrahlung. The results are obtained for an idealized luminosity measurement and make use of the structure function method for differential cross sections. A comparison is made to two fashionable event generators.