The line profiles of a dozen series of widely different appearance, observed recently in the rare-gas optical absorption spectra between 20 and 100 eV, are analyzed by adapting and extending previously developed theory. Theory characterizes each profile by its linewidth, q index, and correlation coefficient ρ and relates these parameters to matrix elements of the energy and of the electric dipole moment. Because the profiles result from interference effects, the signs of these matrix elements are highly relevant. Crude estimates of such, hitherto hardly accessible, matrix elements are obtained from experimental evidence and from atomic theory, and are intercompared and found to be in general agreement. Similarities and differences among the line profiles are thereby tentatively explained. The connection of Rydberg series and absorption edges is discussed and the occurrence of downward jumps at some edges is explained. This exploratory investigation demonstrates how one can treat experimental data, and it surveys the kind and volume of information on the dynamics of highly and multiply excited atoms made accessible by recent experimental techniques.