In July 1971 a report on 'An Experimental, Comprehensive Flare Index and its Derivation for 'Major' Flares, 1955-1969' was published by the present authors as Report UAG-14 of World Data Center A for Solar-Terrestrial Physics. The index apparently proved to be a useful tool for some investigators, and values of the indices for the later years, 1970-1974, were published in Report UAG-52, 'Experimental Comprehensive Solar Flare Indices for Certain Flares, 1970-1974'. Requests have been received for values of the Comprehensive Flare Index (CFI) for still later years. Accordingly, the present report has been prepared for 1975 through 1979, years that complete data for solar cycle 20 and provide information for the ascending branch of cycle 21. (For November-December 1979, it was necessary to use preliminary summaries of flare data. Final Ha flare evaluations were not available for these months at the time of preparation of this report.)