New basis sets, acyXz-J (X = 2, 3, 4), were designed for tellurium and selenium atoms for the calculation of indirect nuclear spi- spin coupling constants involving selenium or tellurium nuclei. Saturation of angular spaces was performed in an even-tempered manner till achieving the convergence of spin spin coupling constants under consideration. The high-accuracy correlated SOPPA(CCSD) method was employed in this procedure. Saturated basis sets were contracted by approximately 30% using the coefficients obtained from the atomic self-consistent field (SCF) closed-shell calculations of selenium and tellurium anions, Se2- and Te2-. Final basis sets of acyXz-J showed sufficiently high accuracy in comparison with previous special basis sets.