We have investigated the inverse electron-demand Diels-Alder reactions of trans-cyclooctene (TCO) and endo-bicyclo[6.1.0]nonyne (BCN) with a 1,2,4,5-tetrazine, a cyclopentadienone, and an ortho-benzoquinone. Tetrazines react significantly faster with TCO compared to BCN because the highest occupied molecular orbital (HOMO) of TCO is significantly higher in energy than the HOMO of BCN and there is less distortion of the tetrazine. Despite the different HOMO energies, TCO and BCN have similar reactivities toward cyclopentadienones, while BCN is significantly more reactive than TCO in the cycloaddition with orthobenzoquinone. We find that the higher reactivity of BCN compared to TCO with ortho-benzoquinone is due to secondary orbital interactions of the BCN HOMO-1 with the diene LUMO.