  We present an analysis of spectroscopic radial velocity and photometric data
of three bright Galactic Cepheids: LR Trianguli Australis (LR TrA), RZ Velorum
(RZ Vel), and BG Velorum (BG Vel). Based on new radial velocity data, these
Cepheids have been found to be members of spectroscopic binary systems.
  The ratio of the peak-to-peak radial velocity amplitude to photometric
amplitude indicates the presence of a companion for LR TrA and BG Vel. IUE
spectra indicate that the companions of RZ Vel and BG Vel cannot be hot stars.
  The analysis of all available photometric data revealed that the pulsation
period of RZ Vel and BG Vel varies monotonically, due to stellar evolution.
Moreover, the longest period Cepheid in this sample, RZ Vel, shows period
fluctuations superimposed on the monotonic period increase. The light-time
effect interpretation of the observed pattern needs long-term photometric
monitoring of this Cepheid. The pulsation period of LR TrA has remained
constant since the discovery of its brightness variation.
  Using statistical data, it is also shown that a large number of spectroscopic
binaries still remain to be discovered among bright classical Cepheids.
