A procedure is presented to improve on measurement of total H I fluxes for extended sources in the Arecibo Legacy Fast Arecibo L-band Feed Array (ALFALFA) survey of neutral hydrogen sources in the nearby universe. A number of tests of the procedure are detailed, and we verify that we recover all of the flux measured with much larger telescope beams. Total fluxes are reported for all sources (1) exceeding 10 Jy km/s in the {alpha}.100 catalog (Haynes et al. 2018ApJ...861...49H), or (2) with Uppsala General Catalog (Cat. VII/26) diameters 3.0 arcmin or more, or (3) ALFALFA pipeline isophotal ellipse area more than 3.0 times the Arecibo beam. Total fluxes are also provided for a number of confused pairs and small groups including one or more of those high-flux sources. These data should be of use in baryonic Tully-Fisher studies and other applications where the measurement of the total reservoir of neutral atomic gas is important.