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° from the orbital inclination. While some of these data sets 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.