Quantitative results for 49 visibility fades observed from College, Alaska, during 1965 are presented. A majority of the fades revealed ionospheric optical depths in excess of unity at 68 MHz. Optical depth is numerically equal to mean‐square fluctuation in radio‐frequency phase across a plane at the base of the scattering region; thus, the fades often were characterized by rms phase deviations in excess of one radian at 68 MHz. The wavefront phase structure immediately after scattering was found to have scales in the range of tens and hundreds of meters. The observations usually were not consistent with the demands of a Gaussian autocorrelation function, as is commonly assumed. Rather, the perturbed wavefronts displayed evidence of quasi‐periodic structure in the observed dimensional range.