  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
$>3\rm{M}_{\odot}$), the possible donor mass is
$\approx$0.5--$1.4\rm{M}_{\odot}$, the inclination is
$\approx{40}^\circ$--$60^\circ$ and the distance is $\approx$8--12\,kpc. The
corresponding mass of the compact object is $\approx$4--$11\rm{M}_{\odot}$. We
then confirm a previous estimate that the theoretical conservative mass
transfer rate in GX 339--4 is $\lesssim{10^{-9}}\rm{M}_{\odot}$ yr$^{-1}$. This
is $\gtrsim$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 $\sim$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 $\sim$10 yr, which appears consistent with
the observations. The other solution invokes non-conservative mass transfer.
This requires that $\approx$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.
