  The PICsIT detector onboard the INTEGRAL satellite was designed to provide
information about emission in the soft gamma-ray band for many bright sources.
Due to strong and variable instrumental background, only 4 objects have been
detected so far using standard software. The moderate sensitivity of PICsIT can
be compensated for in the case of many objects by adopting a long exposure
time, thanks to INTEGRAL's large field of view. With angular resolution far
higher than that of all other instruments operating in a similar energy band,
PICsIT is suitable for fields too crowded or too significantly affected by
Galactic diffuse emission. Therefore, it is desirable to improve the spectral
extraction software to both obtain more reliable results and enlarge the number
of objects that can be studied. The new PICsIT spectral extraction method is
based on three elements: careful modelling of the background, an
energy-dependent pixel-illumination function, and the computation of the
probability density of the source count rate. The most important element is the
proper treatment of the Poisson-distributed data, developed within a Bayesian
framework. The new method was tested extensively on both a large true data set
and simulated data. Results assumed in simulations were reproduced perfectly,
without any bias and with high precision. Count rates measured for Crab were
far more stable than those obtained with the standard software. For weaker
sources, the new method produced spectra of far higher quality and allows us to
detect at least 8 additional objects. Comparison with other INTEGRAL
instruments demonstrated that PICsIT is well calibrated and provides valuable
information about the continuum emission in the 250 keV -- 1 MeV band.
