Four Be stars, HR 1960, HR 2968, HR 3237 and HR 3642, selected according to their periodic variations in Hipparcos and Geneva photometries, were monitored from 1998 until 2001 with the CORALIE spectrograph. Among these stars, two are new spectroscopic binaries and one is a new lambda Eri short period variable. HR 1960 is a low amplitude (K = 3.4 km s(-1)) SB1 with a period of 395.48 d in agreement with the photometric prediction. HR 3237 is a short period SB1 (P = 5.1526 d). HR 3642 presents some interesting variations in photometry and spectroscopy: indeed, a mid- and a short-term variation is present with periods of 137.99 d (Hp magnitude) and 1.13028 d (radial velocity) respectively. The short-term variation, characteristic of the lambda Eri stars, probably implies non-radial pulsations or inhomogeneities in the corotating disc. The last star, HR 2968, is an excellent photometric binary candidate, but no spectroscopic obviousness of a companion has been found.