The solution to the equation for the diffusion of lead and uranium from a sphere, including the effect of a pulse of metamorphism, is applied to the problem of discordant U-Pb ages. It is found that a pulse of metamorphism can greatly disturb the straight-line pattern found by Tilton, and the implications of this with regard to the thermal history of zircons are discussed. The effect of pure U diffusion is found to be to generate a straight-line pattern having a different slope from that for pure Pb diffusion. A very small amount of U diffusion combined with Pb diffusion can significantly alter Tilton's straight-line pattern. This effect is relatively insensitive to the magnitude of the U diffusion. The effects of combined U and Pb diffusion with a pulse of metamorphism are found to be too complex to exhibit regularities.