We aim to exploit the available INTEGRAL/SPI data to provide time-averaged spectra of the brightest soft gamma-ray sources. Employing a maximum-likelihood fit technique for our SPI data analysis, we take as input to our source model the source catalog derived by Bouchet et al. (2008) from a SPI all-sky study. We use the first four years of public SPI data and extract spectra between 25 keV and 1 MeV for the 20 catalog sources detected by Bouchet et al. at 200 - 600 keV with >= 2.5 sigma. In order to verify our analysis, we also extract spectra for the same sources from the corresponding INTEGRAL/ISGRI data. We fit adequate spectral models to the energy range 25-1000 keV for SPI and 25-600 keV for ISGRI. We use our spectra from the Crab (which is among the 20 sources studied here) and an empty location in a crowded field to derive an estimation of the systematic errors. The agreement between our SPI and ISGRI measurements is good if we normalise them on the Crab spectrum. Our SPI flux measurements also agree well with those by Bouchet et al. (2008). All 20 sources in our sample are detected independently in the bands 25-100 keV and 100-200 keV. At 200-600 keV we detect eight sources, at 600-1000 keV we detect two sources. Our spectra agree well with the results from previous publications where available. For six of the 14 XRBs in our sample we find evidence for a hard powerlaw-component which becomes dominant above the cutoff energy of the thermal Comptonization component. In two of these cases, our study provides the first indication of such emission. For the others, our results confirm previous studies. Our Crab spectrum (from 1.3 Ms exposure), shows a significant flux in all points and is well described by a powerlaw with a break near 100 keV and spectral indices 2.11 and 2.20. Comment: 24 pages, 44 figures, accepted for publication by A&A