The problem of competition between concerted and stepwise diradical mechanisms in 1,3-dipolar cycloadditions was addressed by studying the reaction between nitrone and ethene with DFT (R(U)B3LYP/6-31G) and post HF methods. According to calculations this reaction should take place via the concerted cycloaddition path. The stepwise process is a viable but not competitive alternative. The R(U)B3LYP/6-31G study was extended to the reaction of the same 1, 3-dipole with cyclobutadiene and benzocyclobutadiene. The very reactive antiaromatic cyclobutadiene has an electronic structure that is particularly disposed to promote stepwise diradical pathways. Calculations suggest that its reaction with nitrone represents a borderline case in which the stepwise process can compete with the concerted one on similar footing. Attenuation of the antiaromatic character of the dipolarophile, i.e., on passing from cyclobutadiene to benzocyclobutadiene, causes the concerted 1,3-dipolar cycloaddition to become once again prevalent over the two-step path. Thus, our results suggest that, in 1,3-dipolar cycloadditions that involve normal dipolarophiles, the concerted path (Huisgen's mechanism) should clearly overwhelm its stepwise diradical (Firestone's mechanism) counterpart.