The galactic black hole candidate Cygnus X-1 is observed to be in one of tw
o X-ray spectral states: either the low/hard (low soft X-ray flux and a fla
t power-law tail) or high/soft (high blackbody-like soft X-ray flux and a s
teep power-law tail) state. The physical origin of these two states is uncl
ear. We present here a model of an ionized accretion disc, the spectrum of
which is blurred by relativistic effects, and fit it to the ASCA, Ginga and
EXOSAT data of Cygnus X-1 in both spectral states. We confirm that relativ
istic blurring provides a much better fit to the low/hard state data and, c
ontrary to some previous results, find the data of both states to be consis
tent with an ionized thin accretion disc with a reflected fraction of unity
extending to the innermost stable circular orbit around the black hole. Ou
r model is an alternative to those that, in the low/hard state, require the
accretion disc to be truncated at a few tens of Schwarzschild radii, withi
n which there is a Thomson-thin, hot accretion flow. We suggest a mechanism
that may cause the changes in spectral state.