Binary companions are often invoked to explain the axial and point symmetry seen in the majority of planetary nebulae and proto-planetary nebulae (PPNs). To explore this hypothesis, we have undertaken a long-term (20 year) study of light and velocity variations in PPNs. From the photometric study of 24 PPNs, we find that all vary in brightness, and from a subset of 12 carbon-rich PPNs of F-G spectral type we find periods of 35-155 days, with the cooler having the longer periods. The variations are seen to be due to pulsation; no photometric evidence for binarity is seen. A radial velocity study of a sub-sample of seven of the brightest of these shows that they all vary with the pulsation periods. Only one shows evidence of a longer-term variation that we tentatively identify as being due to a binary companion. We conclude that the present evidence for the binary nature of these PPNs is meager and that any undetected companions of these PPNs must be of low mass (< 0.25 $M_{odot}$) or long period (> 30 years).