The behaviour and structural performance of imperfect beam-columns with crossarms and externally prestressed cable stays are studied numerically, where the combination of bending and compression is assumed to be derived from the system self-weight acting orthogonally to the applied axial load. Both doubly-symmetric and mono-symmetric systems are studied. Sensitivity of the structural response to varying prestressing levels, pre-cambering and initial imperfections is investigated. Different initial imperfection levels and combinations are considered to facilitate the exploration of interactive buckling. The optimum prestressing force in terms of ultimate resistance and two structural efficiency indicators is also studied. It is found that relatively small crossarm lengths, stay diameters and crossarm length ratios should be avoided. Moreover, mono-symmetric cases are more sensitive to the level of pre-cambering than their doubly-symmetric counterparts. Considering both load-carrying capacity and structural efficiency, doubly-symmetric cases perform best with zero pre-cambering, but mono-symmetric cases perform best with upward pre-cambering. As for the true optimum prestressing levels, these are recommended to be significantly above the linearly obtained optimum to maximize the structural efficiency.