We present an investigation of three chemically peculiar ( CP ) stars and one CP star candidate which exhibit photometric periods below 12 hours . New spectroscopic observations have been acquired which confirm the peculiar nature of all objects . HD 77013 and HD 81076 are classical CP1 ( Am ) stars ; HD 67983 is a marginal CP1 ( Am : ) star , and HD 98000 is a CP2 ( Ap ) star . We have procured observations from the ASAS-3 and SuperWASP archives and obtained additional photometry in order to verify the results from the sky survey data . We have derived astrophysical parameters and investigated the positions of our target stars in the M _ { Bol } versus \log T _ { \mathrm { eff } } diagram , from which information on evolutionary status has been derived . We present period analyses and discuss each object in detail . From the available data , we propose pulsational variability as the underlying mechanism for the variability in HD 67983 , HD 77013 and HD 81076 , which offer the opportunity to study the interaction of atomic diffusion and pulsation . HD 67983 and HD 77013 exhibit multiperiodic variability in the \gamma Doradus frequency realm ; HD 81076 is a \delta Scuti star . The CP2 star HD 98000 exhibits monoperiodic variability with a frequency of f \approx 2.148 c/d ( P \approx 0.466 d ) , which we interpret as the rotational period . If this assumption is correct , HD 98000 is the \alpha ^ { 2 } Canum Venaticorum ( ACV ) variable with the shortest period hitherto observed and thus a very interesting object that might help to investigate the influence of rotational mixing on chemical peculiarities .