The effect of small density asymmetries in an interstellar dust cloud on the process of accretion by the Sun in its passage through the cloud is considered, with particular reference to Lyttleton's theory of the origin of comets. Such variations in density can give the accreted material a velocity component perpendicular to the axis of accretion sufficient to prevent the material falling into the Sun. Nuclei which might form as a result of the disruption of the accreted material into separate segments can be deflected into periodic orbits, thus apparently removing one of the difficulties of Lyttleton's theory. It appears to be unlikely, however, that the steady state considered by Bondi and Hoyle in earlier papers concerning accretion problems would be reached in the presence of asymmetries. Thus their estimates of the rate at which the Sun can gain in mass might need to be considerably reduced. It is also shown that the influence of random magnetic fields on charged particles will tend to reduce the rate of accretion.