We have made a detailed study of the radio-frequency size effect in thin parallel plates of potassium. Both the resistance and reactance anomalies of the surface impedance in a magnetic field have been observed. By careful determination of the sample thickness and using the known dimensions of the Fermi surface of this metal, we have determined which point on the experimentally observed lines corresponds to the cutoff criterion for the extremal orbit. The line shape and linewidths have been measured over a large range of frequency. Linewidths are found to vary as the inverse cube root of the experimental frequency. In a magnetic field tilted out of the sample plane, and with the rf current perpendicular to the field, the size-effect signal is found to shift to increased fields very nearly as 12θ. Using the mode of polarization with the rf current parallel to the field in the tilted-field geometry, we have observed size-effect signals due to the elliptic limiting point. The results of this measurement indicate the absence of the distortion of the potassium Fermi surface predicted by Overhauser.