We present a radial velocity analysis of 20 solar neighbourhood RR Lyrae and three Population II Cepheid variables. We obtained high-resolution, moderate-to-high signal-to-noise ratio spectra for most stars; these spectra covered different pulsation phases for each star. To estimate the gamma (centre-of-mass) velocities of the programme stars, we use two independent methods. The first, `classic' method is based on RR Lyrae radial velocity curve templates. The second method is based on the analysis of absorption-line profile asymmetry to determine both pulsational and gamma velocities. This second method is based on the least-squares deconvolution (LSD) technique applied to analyse the line asymmetry that occurs in the spectra. We obtain measurements of the pulsation component of the radial velocity with an accuracy of ±3.5 km s-1. The gamma velocity was determined with an accuracy of ±10 km s-1, even for those stars having a small number of spectra. The main advantage of this method is the possibility of obtaining an estimation of gamma velocity even from one spectroscopic observation with uncertain pulsation phase. A detailed investigation of LSD profile asymmetry shows that the projection factor p varies as a function of the pulsation phase - this is a key parameter, which converts observed spectral line radial velocity variations into photospheric pulsation velocities. As a by-product of our study, we present 41 densely spaced synthetic grids of LSD profile bisectors based on atmospheric models of RR Lyr covering all pulsation phases.