A complete sample of core-dominated radio sources has been studied using the interplanetary-scintillation method. In total, 72 sources were observed, with scintillations detected in 28 of them. The remaining sources have upper limits on their flux densities. Integrated flux densities are estimated for 24 sources. Cut-offs have been observed in the spectra of many sources. The thermal-electron densities have been estimated, assuming that these cut-offs are due to free-free absorption of the synchrotron radio emission.