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Scattering by small discontinuities in single- or multimode waveguides is expressed concisely by the ‘small-obstacle’ formula, which constitutes a lowest-order approximation, in which only dipole moments are considered and wall interactions are neglected. The present study deals with the general and systematic derivation of self-consistent corrections to this formula, which are then applied to the calculation of the scattering coefficients for a centred and noncentred perfectly conducting sphere in a rectangular waveguide. The noncentred case is analysed in the dipole approximation, whereas both dipole and quadrupole moments are included for the centred case. Results for dominant-mode (H10) operation are compared with measurements, and it is found that the discrepancy between experiment and uncorrected small-obstacle theory is reduced substantially, though not completely, by inclusion of corrections for larger sphere sizes.