Context. Planetary studies demand precise and accurate stellar parameters as input for inferring the planetary properties. Different methods often provide different results that could lead to biases in the planetary parameters. Aims: In this work, we present a refinement of the spectral synthesis technique designed to treat fast rotating stars better. This method is used to derive precise stellar parameters, namely effective temperature, surface gravity, metallicity, and rotational velocity. The procedure is tested for FGK stars with low and moderate-to-high rotation rates. Methods: The spectroscopic analysis is based on the spectral synthesis package Spectroscopy Made Easy (SME), which assumes Kurucz model atmospheres in LTE. The line list where the synthesis is conducted is comprised of iron lines, and the atomic data are derived after solar calibration. Results: The comparison of our stellar parameters shows good agreement with literature values, both for slowly and for fast rotating stars. In addition, our results are on the same scale as the parameters derived from the iron ionization and excitation method presented in our previous works. We present new atmospheric parameters for 10 transiting planet hosts as an update to the SWEET-Cat catalog. We also re-analyze their transit light curves to derive new updated planetary properties. Based on observations collected at the La Silla Observatory, ESO (Chile) with the FEROS spectrograph at the 2.2 m telescope (ESO runs ID 089.C-0444(A), 088.C-0892(A)) and with the HARPS spectrograph at the 3.6 m telescope (ESO runs ID 072.C-0488(E), 079.C-0127(A)); at the Observatoire de Haute-Provence (OHP, CNRS/OAMP), France, with the SOPHIE spectrograph at the 1.93 m telescope and at the Observatoire Midi-Pyrénées (CNRS), France, with the NARVAL spectrograph at the 2 m Bernard Lyot Telescope (Run ID L131N11).Appendix A is available in electronic form at http://www.aanda.org