It is shown that previously proposed expressions for the semiconductor electron-hole product, which purport to separate the influence of carrier degeneracy and bandgap narrowing, fail to properly delineate these effects. A reformulation of the expression in which the two effects are successfully separated is proposed, valid when the majority carrier concentration is independent of bandgap narrowing, as occurs in the common case of low injection and quasi-neutrality. It is shown that under other conditions, the two effects may not be treated in isolation but that only their combined effect or the marginal effect of one or the other on the total electron-hole product may be assessed. Convenient expressions are provided for the latter case. The revised expression provides both conceptual and computational advantages for semiconductor device modelling.