High-quality radial-velocity observations of Procyon A (α CMi, F5 IV) have been obtained with the Birmingham magneto–optical filter spectrometers using the 1.9–m telescopes at SAAO (1988, 1989 and 1990) and Mt Stromlo (1989 only). These data were searched for the presence of an acoustic p-mode spectrum of oscillations. Power spectral analysis of the velocity time-series data show the noise levels obtained from a 2-week run to be around 2 m s–1 rms (per Fourier bin of |$\sim 1\,\mu \text{Hz}).$| The characteristics of these power spectra are consistent with photon noise, implying a null detection of single strong modes at the |$3\,\sigma\, \,\text{level}\,\text{of} \sim 4\,\text{m}\,\text{s}^{-1}\, \text{rms}.$| The power spectra were also studied for possible periodicities due to the presence of equifrequency spaced modes (as seen in the solar p-mode spectrum where |$\Delta\, v\sim 135\,\mu \text{Hz})$| of comparable power to the background noise. While some periodicities were seen they were not reproducible in all three data sets, and thus are probably not of stellar origin. We are unable to confirm the results of Gelly, Grec & Fossat, who reported a value of |$\Delta\, v\sim 80\,\mu \text{Hz}$| for this star, even though our data are roughly of comparable quality. During the observing runs we also observed the Sun at count rates experimentally set to between 30 and 100 times that which we obtained on Procyon, in order to provide a test of our instruments. Analysis of the resulting power spectrum of the best solar data yields a noise per bin of |$\sim 15\,\text{cm}\,\text{s}^{-1},$| comparable with the size of strongest solar p-modes. A search for periodicities in this power spectrum recovers the known solar frequency spacing of |$\Delta\, v\sim 135\,\mu \text{Hz},$| indicating that there are no serious faults in our instrument or analysis.