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The finite element analysis method and a two-dimensional idealization were used to conduct a detailed parametric study of the stresses in and displacement of models of bonded edgewise "combination-materials" type of orthodontic brackets when subjected to loading and constraint conditions that are deemed to be the same as those that exist in vivo. A "combination-materials" type bracket is herein defined as one in which different materials are used in fabricating the main body and the archwire slot. The present study was conducted in three parts. In Part 1, 16 model cases were analyzed, involving 4 different combinations of materials (for the main body of the bracket and its archwire slot) and 4 different overall bracket configurations (comprising main body, base and slot). The focus of Part 2 was the model bracket configuration that was, on the basis of Part 1 results, deemed to show the "optimum performance". In this part, the parameter investigated was the value of the modulus of elasticity of the adhesive, Eadh. In Part 3, the concept of an efficiency index of the bonded bracket-archwire system, eta, was introduced and explained. The dependence of eta on stated characteristics of a rectangular archwire, for the "optimum performance" model, was explored. Part 1 results led to the conclusion that the "optimum performance" model has equally angulated buccal and lingual edges and the main body and archwire slot are fabricated from glass fiber-reinforced polycarbonate and stainless steel, respectively. Part 2 results showed that, for the aforementioned "optimum performance" model, the longitudinal displacement of the archwire slot is fairly insensitive to Eadh. Part 3 results showed that eta is intimately related to each of the wire characteristics studied (namely cross-sectional dimensions, "interbracket distance" and modulus of rigidity of the material).