Dear Editor, please find enclosed our manuscript on an experimental investigation of sub- Doppler laser cooling of single atoms in optical dipole traps. Since the late 1980s, polarization gradient cooling (PGC) has been the workhorse technique to laser cool neutral atoms to temperatures below the Doppler limit. While PGC has been originally developed for free atoms, it has also been extensively used for confined atoms. However, in optical traps the trapping potential can strongly affect the cooling dynamics and the achievable temperatures. Although of high practical relevance, the influence of the trap on PGC is relatively unreported. In this work, we report on the dependence of the cooling limit on the polarization of the optical trap. We find that PGC works well in a linearly polarized trap but is strongly inhibited for circularly polarization. This behavior is quantitatively explained with the analogy between the ac Stark shift induced by the optical trap and the Zeeman shift in a magnetic field for which the inhibition of PGC is well known. In addition, we investigate practical aspects of PGC and show (1) high sensitivity to polarization impurities and (2) dynamical control of the trap polarization without inducing significant heating. Our results complement previous work on PGC and are of practical importance for the scientific community. We feel that the manuscript could be interesting to the audience of Physical Review A, and therefore ask for your kind consideration. With Best Regards on behalf of all authors, Possible referees: Steven Rolston, University of Maryland - rolston@umd.edu Andrea Alberti, University of Bonn - alberti@iap.uni-bonn.de Cindy Regal, University of Colorado - regal@colorado.edu Mikkel Andersen, University of Otago - mikkel.andersen@otago.ac.nz