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The multi-frequency Sedentary Survey is a flux limited, statisticallywell-defined sample of highly X-ray dominated BL Lacertae objects (HBLs) whichincludes 150 sources. In this paper, the third of the series, we report theresults of a dedicated optical spectroscopy campaign that, together withresults from other independent optical follow up programs, led to thespectroscopic identification of all sources in the sample. We carried out asystematic spectroscopic campaign for the observation of all unidentifiedobjects of the sample using the ESO 3.6m, the KPNO 4m, and the TNG opticaltelescopes. We present new identifications and optical spectra for 76 sources,50 of which are new BL Lac objects, 18 are sources previously referred as BLLacs but for which no redshift information was available, and 8 are broademission lines AGNs. We find that the multi-frequency selection technique usedto build the survey is highly efficient (about 90%) in selecting BL Lacsobjects. We present positional and spectroscopic information for all confirmedBL Lac objects. Our data allowed us to determined 36 redshifts out of the 50new BL Lacs and 5 new redshifts for the previously known objects. The redshiftdistribution of the complete sample is presented and compared with that ofother BL Lacs samples. For 26 sources without recognizable absorption features,we calculated lower limits to the redshift using a method based on simulatedoptical spectra with different ratios between jet and galaxy emission. For asubsample of 38 object with high-quality spectra, we find a correlation betweenthe optical spectral slope, the 1.4 GHz radio luminosity, and the Ca H&K breakvalue, indicating that for powerful/beamed sources the optical light isdominated by the non-thermal emission from the jet.

The Sedentary Survey of Extreme High Energy Peaked BL Lacs III. Results from Optical Spectroscopy