We use simultaneous Swift and RXTE observations of the black hole binary GX 339-4 to measure the inner radius of its accretion disk in the hard state down to 0.4% L_{Edd} via modeling of the thermal disk emission and the relativistically broadened iron line. For the luminosity range covered in this work, our results rule out a significantly truncated disk at 100-1000 R_g as predicted by the advection-dominated accretion flow paradigm. The measurements depend strongly on the assumed emission geometry, with most results providing no clear picture of radius evolution. If the inclination is constrained to roughly 20 degrees, however, the measurements based on the thermal disk emission suggest a mildly receding disk at a luminosity of 0.4% L_{Edd}. The iron abundance varies between roughly 1-2 solar abundances, with the i=20 degrees results indicating a negative correlation with luminosity, though this is likely due to a change in disk illumination geometry.
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