We present first results from contemporaneous observations of Cygnus X-1 with INTEGRAL and RXTE , made during INTEGRAL ’ s performance verification phase in 2002 November and December . Consistent with earlier results , the 3–250 keV data are well described by Comptonization spectra from a Compton corona with a temperature of kT \sim 50 –90 keV and an optical depth of \tau \sim 1.0 –1.3 plus reflection from a cold or mildly ionized slab with a covering factor of \Omega / 2 \pi \sim 0.2 –0.3 . A soft excess below 10 keV , interpreted as emission from the accretion disk , is seen to decrease during the 1.5 months spanned by our observations . Our results indicate a remarkable consistency among the independently calibrated detectors , with the remaining issues being mainly related to the flux calibration of INTEGRAL .