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 INTEGRALs 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.
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