Context : The influence of binarity on the late stages of stellar evolution . Aims : While the first binary post-AGB stars were serendipitously discovered , the distinct characteristics of their Spectral Energy Distribution ( SED ) allowed us to launch a more systematic search for binaries . We selected post-AGB objects which show a broad dust excess often starting already at H or K , pointing to the presence of a gravitationally bound dusty disc in the system . We started a very extensive multi-wavelength study of those systems and here we report on our radial velocity and photometric monitoring results for six stars of early F type , which are pulsators of small amplitude . Methods : To determine the radial velocity of low signal-to-noise time-series , we constructed dedicated auto-correlation masks based on high signal-to-noise spectra , used in our published chemical studies . The radial velocity variations were subjected to detailed analysis to differentiate between pulsational variability and variability due to orbital motion . When available , the photometric monitoring data were used to complement the time series of radial velocity data and to establish the nature of the pulsation . Finally orbital minimalisation was performed to constrain the orbital elements . Results : All of the six objects are binaries , with orbital periods ranging from 120 to 1800 days . Five systems have non-circular orbits . The mass functions range from 0.004 to 0.57 M _ { \odot } and the companions are likely unevolved objects of ( very ) low initial mass . We argue that these binaries must have been subject to severe binary interaction when the primary was a cool supergiant . Although the origin of the circumstellar disc is not well understood , the disc is generally believed to be formed during this strong interaction phase . The eccentric orbits of these highly evolved objects remain poorly understood . In one object the line-of-sight is grazing the edge of the puffed-up inner rim of the disc . Conclusions : These results corroborate our earlier statement that evolved objects in binary stars create a Keplerian dusty circumbinary disc . With the measured orbits and mass functions we conclude that the circumbinary discs seem to have a major impact on the evolution of a significant fraction of binary systems .