The effect of thermodiffusion on dopant distribution in the melt and in the grown crystal is investigated numerically for a vertical Bridgman configuration for situations of pure thermal convection corresponding to dilute alloys. The dopant distribution is shown to be significantly affected by the Soret parameter value. The sensitivity of the system to a variety of parameters, including the Grashof number and the so-called furnace residence time, i.e. the time during which the crucible is maintained in the furnace before initiating the solidification process, is assessed by means of parametric simulations. Moreover, the results indicate that variations in the sign of the Soret parameter can lead to diametrically opposite behaviors, while an increase in the intensity of the thermal convection generally leads to a mitigation of the effects induced by thermodiffusion. On the basis of the numerical results some useful criteria are drawn which could help crystal growers to discern the complex interrelations among the various parameters under one's control (that are not independent of one another) and to elaborate rational guidelines relating to strategies to be used to improve the quality of the resulting crystals.