The phase behaviours and dielectric properties of the plastic phases of several cyclic and branched alcohols have been studied up to pressures of 300 MPa and frequencies to 13 MHz. High values for the static permittivity are found for the liquid and the solid phases below the melting curve. For these compounds the dielectric relaxation occurs at relatively low frequencies. The loss curves have been fitted to modified Debye equations and expressions of Jonscher and Dissado & Hill. The temperature and pressure dependence of the dielectric relaxation time enables us to determine the activation enthalpy and volume, respectively. The activation quantities and parameters for the spectral shape functions of the cyclic and branched alcohols are compared and discussed.