[en] Shell-model calculations are performed for the odd- and even-parity states of ³⁹Cl and the odd-parity states of ³⁹S. The ³⁹S odd-parity states and the ³⁹Cl even-parity states were considered in full (1s,0d)²⁰(0f,1p)³ and (1s,0d)²¹(0f,1p)² configurational spaces, respectively. For the ³⁹Cl odd-parity states it was necessary to use a highly truncated (1s,0d)²⁰(0f,1p)³ configurational space. The method and results of truncation are discussed in some detail. Observables calculated include energy spectra, binding energies, ⁴⁰Ar→³⁹Cl+p spectroscopic factors, first-forbidden and allowed β^- decay of ³⁹S, and γ transitions in both ³⁹S and ³⁹Cl. Results are compared to experiment. For example, the spectroscopic factors for 1/2⁺ and 3/2⁺³⁹Cl states and the γ transitions between the even-parity ³⁹Cl states are predicted with high accuracy while the half-life of ³⁹S is calculated to be 5.6 s (if the spin-parity of ³⁹S has the preferred value of 7/2^-) as compared to the experimental value of 11.5±0.5 s