  [abridged] We attempt to improve on the characterization of the properties
(orbital elements, masses) of two Doppler-detected sub-stellar companions to
the nearby G dwarfs HD 131664 and HD 43848. We carry out orbital fits to the
Hipparcos IAD for the two stars, taking advantage of the knowledge of the
spectroscopic orbits, and solving for the two orbital elements that can be
determined in principle solely by astrometry, the inclination angle $i$ and the
longitude of the ascending node $\Omega$. A number of checks are carried out in
order to assess the reliability of the orbital solutions thus obtained. The
best-fit solution for HD 131664 yields $i=55\pm33$ deg and $\Omega=22\pm28$
deg. The resulting inferred true companion mass is then $M_c = 23_{-5}^{+26}$
$M_J$. For \object{HD 43848}, we find $i=12\pm7$ deg and $\Omega=288\pm22$ deg,
and $M_c = 120_{-43}^{+167}$ $M_J$. Based on the statistical evidence from an
$F$-test, the study of the joint confidence intervals of variation of $i$ and
$\Omega$, and the comparison of the derived orbital semi-major axes with a
distribution of false astrometric orbits obtained for single stars observed by
Hipparcos, the astrometric signal of the two companions to HD 131664 and HD
43848 is then considered detected in the Hipparcos IAD, with a level of
statistical confidence not exceeding 95%. We constrain the true mass of HD
131664b to that of a brown dwarf to within a somewhat statistically significant
degree of confidence ($\sim2-\sigma$). For HD 43848b, a true mass in the brown
dwarf regime is ruled out at the $1-\sigma$ confidence level. [abridged]
