In the first part (pp. 461-478 in this issue) of this study regarding the histamine H2 receptor agonistic binding site, the best possible interactions of histamine with an alpha-helical oligopeptide, mimicking a part of the fifth transmembrane alpha-helical domain (TM5) of the histamine H2 receptor, were considered. It was established that histamine can only bind via two H-bonds with a pure alpha-helical TM5, when the binding site consists of Tyr182/Asp186 and not of the Asp186/Thr190 couple. In this second part, two particular three-dimensional models of G-protein-coupled receptors previously reported in the literature are compared in relation to agonist binding at the histamine H2 receptor. The differences between these two receptor models are discussed in relation to the general benefits and limitations of such receptor models. Also the pros and cons of simplifying receptor models to a relatively easy-to-deal-with oligopeptide for mimicking agonistic binding to an agonistic binding site are addressed. Within complete receptor models, the simultaneous interaction of histamine with both TM3 and TM5 can be analysed. The earlier suggested three-point interaction of histamine with the histamine H2 receptor can be explored. Our results demonstrate that a three-point interaction cannot be established for the Asp98/ Asp186/Thr190 binding site in either of the investigated receptor models, whereas histamine can form three H-bonds in case the agonistic binding site is constituted by the Asp98/Tyr182/Asp186 triplet. Furthermore, this latter triplet is seen to be able to accommodate a series of substituted histamine analogues with known histamine H2 agonistic activity as well.