  We report results of a spectroscopic campaign carried out at the 10 m Gran
Telescopio Canarias for a sample of 22 BL Lac objects detected (or candidates)
at TeV energies, aimed to determine or constrain their redshift. This is of
fundamental importance for the interpretation of their emission models, for
population studies and also mandatory to study the interaction of high energy
photons with the extragalactic background light using TeV sources. High
signal-to-noise optical spectra in the range 4250 - 10000 {\AA} were obtained
to search for faint emission and/or absorption lines from both the host galaxy
or the nucleus. We determine a new redshift for PKS 1424+240 (z = 0.604) and a
tentative one for 1ES 0033+595 (z = 0.467). We are able to set new
spectroscopic redshift lower limits for other three sources on the basis of Mg
II and Ca II intervening absorption features: BZB J1243+3627 (z > 0.483), BZB
J1540+8155 (z > 0.672), and BZB 0J2323+4210 (z > 0.267). We confirm previous
redshift estimates for four blazars: S3 0218+357 (z = 0.944), 1ES 1215+303 (z =
0.129), W Comae (z = 0.102), and MS 1221.8+2452 (z = 0.218). For the remaining
targets, in seven cases (S2 0109+22, 3C 66A, VER J0521+211, S4 0954+65, BZB
J1120+4214, S3 1227+25, BZB J2323+4210), we do not validate the proposed
redshift. Finally for all sources of still unknown redshift, we set a lower
limit based on the minimum equivalent width of absorption features expected
from the host galaxy.
