We study J/ψ production in pp collisions at \sqrt{s}=1.96 and 7 TeV using the colour-singlet model (CSM), including next-to-leading order (NLO) corrections and dominant α5S contributions (NNLOsstarf). We find that the CSM reproduces the existing data if the upper range of the NNLOsstarf is near the actual--but presently unknown--NNLO. The direct yield polarization for the NLO and NNLOsstarf is increasingly longitudinal in the helicity frame when PT gets larger. When one combines the direct yield with a data-driven range for the polarization of J/ψ from χc, the prompt J/ψ polarization yield polarization in the CSM gets significantly closer to the experimental data from the CDF collaboration.