The cycloaddition reactions of 18 1,3-dipolar molecules to ethylene and acetylene have been reinvestigated by quantum chemical methods that are based on a second-order perturbation treatment of electron correlation. It is found that SCS-MP2 and the new perturbative B2-PLYP density functional provide accurate reaction barriers and outperform MP2 as well as standard density functionals such as B3-LYP. The new second-order based methods have the additional advantage that they perform better with increasing quality of the one-particle space, as is desired for a good quantum chemical method. The errors for the reaction enthalpies are in general larger than for the barriers when compared to CBS-QB3 literature values, which is related to stron- chan-es in the electronic structures, but the deviations are again smaller than with MP2 or B3-LYP and are also more systematic. The results of a detailed basis set study suggest that properly polarized triple- AO basis sets represent a good compromise between accuracy and computational speed. The combination of very inaccurate density functionals with small (double-zeta) basis sets, which yields good results for the initial part of the reactions due to error compensation, is not recommended.