We consider constraints on the distance, inclination and component masses in the X-ray binary GX 339-4 resulting from published works, and then construct detailed evolutionary models for the donor. From both considerations, and assuming the black-hole nature for the compact object (i.e., its mass > 3M ), the possible donor mass is ≈0.5-1.4M , the inclination is ≈ 40 • -60 • and the distance is ≈8-12 kpc. The corresponding mass of the compact object is ≈4-11M . We then confirm a previous estimate that the theoretical conservative mass transfer rate in GX 339-4 is 10 −9 M yr −1 . This is 10 times lower than the average mass accretion rate estimated from the long-term X-ray light curve. We show that this discrepancy can be solved in two ways. One solution invokes irradiation of the donor by X-rays from accretion, which can temporarily enhance the mass transfer rate. We found that absorption of a ∼1 per cent of the irradiating luminosity results in the transfer rate equal to the accretion rate. The time scale at which the transfer rate will vary is estimated to be ∼10 yr, which appears consistent with the observations. The other solution invokes non-conservative mass transfer. This requires that ≈70 per cent of the transferred mass escapes as a strong outflow and carries away the specific angular momentum comparable to that of the donor.