  We present the analysis of an extended \textit{INTEGRAL} dataset of the
high-mass microquasar Cygnus X-1. We first classify, in a model-independent
way, all the \textit{INTEGRAL} individual pointings taken between 2003 and 2016
in three basic spectral states. This, in particular, allows us to triple the
exposure time of the soft state in comparison with previous publication. We
then study the spectral properties of the 5--400 keV stacked spectra of the
soft and hard states and provide the parameters obtained with our modelling.
Using a refined alternative method of extracting the Compton double events of
the IBIS telescope, we then extract high-energy ($>$400 keV) spectra in the two
states. We do detect an hard tail in both states. Our refined analysis allows
us to obtain a hard state (count) spectrum at a flux lower than previously
published by our team. Although a full estimate of the calibration property of
this improved software is still needed, this seems to be more inline with the
hard state hard tail seen with other instruments.
