We study the orbital modulation of X-rays from Cyg X-3, using data from Swift, INTEGRAL and RXTE. Using the wealth of data presently available and an improved averaging method, we obtain energy-dependent folded and averaged light curves with unprecedented accuracy. We find that above ∼5 keV the modulation depth decreases with increasing energy, which is consistent with the modulation being caused by both bound–free absorption and Compton scattering in the stellar wind of the donor, with minima corresponding to the highest optical depth, which occurs around the superior conjunction. We find a decrease of the depth below ∼3 keV, which appears to be due to re-emission of the absorbed continuum by the wind in soft X-ray lines. Based on the shape of the folded light curves, any X-ray contribution from the jet in Cyg X-3, which emits γ-rays detected at energies >0.1 GeV in the soft spectral states, is found to be minor up to ∼100 keV. This implies the presence of a rather sharp low-energy break in the jet MeV-range spectrum. We also calculate phase-resolved RXTE X-ray spectra and show that the difference between the spectra corresponding to phases around superior and inferior conjunctions can indeed be accounted for by the combined effect of bound–free absorption in an ionized medium and Compton scattering.