We discuss one-loop radiative corrections to the sphaleron-induced baryon number-violating transition rate near the electroweak phase transition in the standard model. We emphasize that in the case of a first-order transition a rearrangement of the loop expansion is required close to the transition temperature. The corresponding expansion parameter, the effective 3-dimensional gauge coupling approaches a finite $λ$ dependent value at the critical temperature. The $λ$ (Higgs mass) dependence of the 1-loop radiative corrections is discussed in the framework of the heat kernel method. Radiative corrections are small compared to the leading sphaleron contribution as long as the Higgs mass is small compared to the W mass. To 1-loop accuracy, there is no Higgs mass range compatible with experimental limits where washing-out of a B+L asymmetry could be avoided for the minimal standard model with one Higgs doublet.

17 pages, RevTeX, (4 figures in a separate uuencoded file), HD-THEP-93-23rev