© 2017 IEEE. The Canted-Cosine-Theta (CCT) technology has the potential, by its intrinsic stress-management, to lower coil stresses in high-field accelerator magnets. This is especially relevant for Nb3Sn magnets, which may be subject to irreversible degradation if the coil stresses exceed critical values. The internal structure of CCT coils, however, dilutes the engineering current density. For an efficient design, the internal structure, therefore, needs to be reduced to the limit given by the computer-numerical-control machining capabilities. In that case, however, additional mechanical stiffness must be provided by an external mechanical structure. The mechanical structure for the Paul Scherrer Institut (PSI) CCT program, which is described in this paper, is based on the bladder and key concept. The CCT-specific deviations from the prevalent bladder and key implementations are discussed. In addition, a two-dimensional and three-dimensional analysis in all stages of loading, cooling, and powering of the first PSI magnet prototype, as well as a tolerance analysis, is reported.