We study orbital modulation of X-rays from Cyg X-3, using data from Swift, INTEGRAL and RXTE. Using the wealth of the presently available data 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 the 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 gamma-rays detected at energies >0.1 GeV in 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 the difference between the spectra corresponding to phases around the superior and inferior conjunctions can indeed be accounted for by a combined effect of bound-free absorption in an ionized medium and Compton scattering.