We solve analytically the problem of dopant redistribution from an arbitrary initial implanted profile. The diffusivity, assumed concentration independent, can be an otherwise arbitrary function of temperature. Next, we derive a closed-form expression for the annealed concentration distribution in the special case of an initial truncated Gaussian. Our solution is valid over a much wider range of experimental conditions than is Seidel and MacRae's approximation [Trans. AIME 245, 491 (1969)]. We offer a simple, yet precise, criterion for the validity of this approximation, and we guard against its indiscriminate use. Last, we fit short-time annealed P profiles in implanted Si to get an average diffusivity D̄≅3×10-12 cm2/s. We describe simple and accurate one-parameter data-fitting procedures.