The Lewis acid-mediated [3 + 2] cycloaddition of N-sulfonyl- and N-sulfamoylaziridines with alkenes provides a rapid and efficient access to 1-azaspiro[4.n]alkanes. Experimental studies have been combined with DFT calculations to explore the mechanism of the reaction. They demonstrate that the nature of the electron-withdrawing nitrogen protecting group has a very limited influence on the course of the reaction and, particularly, on the initial formation of the 1,3-zwitterionic species through C-N bond cleavage, which has been found to be the rate-determining step. Compared to N-sulfonylaziridines, N-sulfamoylaziridines have proved to be more synthetically useful synthons that afford crystalline polycyclic structures in good yields. A short sequence of catalytic C(sp(3))-H amination-cyclization-[3 + 2] cycloaddition has then been successfully designed to afford the homologue 1-azaspiro[5.n]alkanes, thereby illustrating the higher versatility of sulfamates in these cycloadditions.