In the ductile-to-brittle transition temperature range, a marked effect of specimen thickness on fracture toughness sometimes can be seen. A number of experimental results indicate a decrease in fracture toughness with increasing specimen thickness. There are two explanations for the effect of thickness in fracture toughness. One explanation is the traditional understanding that larger thickness produces a higher crack-tip constraint. Another is associated with the statistical nature of cleavage fracture: an increase in thickness brings about an increase in the probability of involving embrittled microstructures. The latter is called the weakest link size effect. In this paper, the contributions to these two explanations of the effect of thickness in fracture toughness are compared for structural steels.