Dibenzoannulated cyclooctynes have emerged as valuable compounds for bioorthogonal reactions. They are commonly used in combination with azides in strain-promoted 1,3-dipolar cycloadditions. They are typically, however, unreactive towards 3,6-disubstituted tetrazines in inverse electron-demand Diels-Alder cycloadditions. Recently a dibenzoannulated bicyclo[6.1.0]nonyne derivative (DMBO) with a cyclopropane fused to the cyclooctyne core was described, which showed surprising reactivity towards tetrazines. To elucidate the unusual reactivity of DMBO, we performed density functional theory calculations and revealed that a tub-like structure in the transition state results in a much lower activation barrier than in the absence of cyclopropane fusion. The same transition state geometry is found for different cycloalkanes fused to the cyclooctyne core albeit higher activation barriers are observed for increased ring sizes. This conformation is energetically unfavored for previously known dibenzoannulated cyclooctynes and allows tetrazines and azides to approach DMBO from the face rather than the edge, a trajectory that was hitherto not observed for this class of activated dieno- and dipolarophiles.