  We present models of the shapes of four Kuiper belt objects (KBOs) and Jovian
Trojan (624) Hektor as ellipsoidal figures of equilibrium and Roche binaries.
Our simulations select those figures of equilibrium whose lightcurves best
match the measured rotational data. The best fit shapes, combined with the
knowledge of the spin period of the objects provide estimates of the bulk
densities of these objects. We find that the lightcurves of KBOs (20000) Varuna
and 2003 EL61 are well matched by Jacobi triaxial ellipsoid models with bulk
densities 992 (-15,+86) kg/m^3 and 2551 (-10,+115) kg/m^3, respectively. The
lightcurves of (624) Hektor and KBO 2001 QG298 are well-described by Roche
contact binary models with densities 2480 (-80,+292) kg/m^3 and 590 (-47,+143)
kg/m^3, respectively. The nature of 2000 GN171 remains unclear: Roche binary
and Jacobi ellipsoid fits to this KBO are equivalent, but predict different
densities, ~2000 kg/m^3 and ~650 kg/m^3, respectively. Our density estimates
suggest a trend of increasing density with size.
