We present measurements of the total interaction cross section and of the single-diffractive dissociation cross section in αα collisions at √ s = 126 GeV. The result obtained for the total cross section, σ tot = (315±18) mb, is a substantial improvement on the precision of earlier measurements. Earlier elastic data were re-analysed, incorporating, through the optical theorem, the present σ tot measurement, resulting in improved determinations of the forward slope, b − t <0.07 = (87±4) GeV −2 , and of the integrated elastic cross section, σ el = (58±6) mb. The single-diffractive differential cross section falls exponentially with momentum transfer at small values of t with a slope b sd = (19.3 ± 0.6) GeV −2 . The integrated single-diffractive cross section is σ sd = (16.6±2.5) mb. The topology of charged tracks resulting from the disintegration of the α in single-diffractive events reveals a two-component distribution. The cross section data are compared with multiple-scattering models.