The use of an embedded-process zone (EPZ) model to investigate the mode I cohesive parameters for plastically-deforming, adhesively-bonded joints is demonstrated in this paper. It is shown that for the particular systems investigated, the cohesive parameters are consistent with an adhesive layer deforming in accordance with its bulk constitutive properties (as constrained by the adherends). In other words, these systems provide examples where the cohesive tractions exerted by an adhesive layer can be calculated simply from considerations of the constrained deformation of the adhesive. Consistent with such calculations, the peak stress in the adhesive layer decreases as the level of the constraint decreases (either with an increase in the thickness of the adhesive layer or with a decrease in the thickness of the adherends). It is also shown that owing to a compensating effect in which the critical displacement for failure varies with the constraint, the energy absorbed by the adhesive layer (the 'intrinsic' toughness of the joint) is essentially independent of the geometry in these systems.