We present the results of the analysis of the broad-band spectrum of C
ygnus X-1 from 3.0 to 200 keV, using data from a 10 ksec observation b
y the Rossi X-ray Timing Explorer. Although the spectrum can be well d
escribed phenomenologically by an exponentially cut-off power law (pho
ton index Gamma = 1.45(-0.02)(+0.01), e-folding energy E-f = 162(-8)(9) keV, plus a deviation from a power law that formally can be modeled
as a thermal blackbody with temperature kT(BB) = 1.2(+0.0)(-0.1) keV)
, the inclusion of a reflection component does not improve the fit. As
a physical description of this system, we apply the accretion disc co
rona (ADC0 models of Dove. Wilms Sr Begelman [1]. A slab-geometry ADC
model is unable to describe the data. However, a spherical corona, wit
h a total optical depth tau = 1.6 +/- 0.1 and an average temperature k
T(C) = 87 +/- 5 keV, surrounded by an exterior cold disc, does provide
a good description of the data (chi(red)(2) = 1.55). These models dev
iate from the data by up to 7% in the 5-10 keV range. However, conside
ring how successfully the spherical corona reproduces the 10-200 keV d
ata, such ''photon-starved'' coronal geometries seem very promising fo
r explaining the accretion processes of Cygnus X-1.