  We attempt to constrain the black hole spin in GX 339-4 from spectral fitting
of disc dominated data using RXTE spectra from the three most recent outbursts.
We use the best current models for the disc emission, including full radiative
transfer through the photosphere rather than assuming that the intrinsic
emission from each radius has a (colour temperature corrected) blackbody
spectrum. The results strongly depend on the poorly known binary system
parameters, but we find a strict upper limit of a<0.9 for any distance greater
than 6 kpc, assuming that the orbital inclination is the same as that of the
inner disc. By contrast, the higher spin of 0.935 +/- 0.01 (statistical)
+/-0.01 (systematic) claimed from fitting the iron line profile in this object
requires that the inner disc is misaligned by over 20 degrees from the orbital
inclination. While some of these datasets are distorted by instrumental pileup,
the same spin/inclination constraints are derived from data which are not piled
up, so there is a real conflict between the two techniques to measure spin. We
argue that the disc spectral fits are more likely to be robust hence that there
are still issues to be understood in the iron line profile.
