Numerous classes of dopant have been added to MgB2 in order to raise the upper critical field, B-c2, and hence to increase the field range over which the pinned superconductor has the possibility of supporting supercurrent. Thus dopant additions to grain-boundary-pinned MgB2, for example, have the effect of raising the high field critical current density, J(c)(B). However, at low fields, when B is relatively small compared to B-c2, J(c)(B) decreases as B-c2 increases. This leads to a low field convergence, or even the intersection, of the J(c)(B) curves of a family of variously doped MgB2 strands. Two important conclusions derive from this "crossover effect'': (i) Doping-induced increases of B-c2 should be applied only if improved high field properties are required. For low field applications of MgB2 such as: low field nuclear magnetic resonance imaging (MRI), synchrotron insertion devices, and current leads, doping should be avoided since not only would the increased B-c2 degrade J(c), but the possible chemical byproducts of doping may reduce connectivity; (ii) If an across-the-board increase in J(c)(B) is desired there is no substitute for increased connectivity, in regard to which densification of the MgB2 layer (the subject of a separate report) is recommended. (C) 2013 Elsevier B.V. All rights reserved.