The complete, incomplete and fission cross sections are being measured for 12,13 C + 208,207 Pb systems to investigate the influence of breakup at abovebarrier energies which form the same compound nucleus at the same excitation energies. The α-active heavy reaction products are measured for most dominant reaction xn-channels along with fission cross sections which originate almost exclusively from the complete fusion (CF). The results from the present systems show substantial components from the incomplete fusion in addition to CF. The CF cross section is suppressed by 12 ± 2% for 12 C and 3 ± 2% for 13 C compared with the single-barrier penetration model calculations. A systematic variation of the suppression of CF for reactions of weakly bound nuclei 6,7 Li, 9 Be, 10,11 B and 12,13 C on targets of 207,208 Pb and 209 Bi is being found as a function of the breakup threshold energy.