Single dish CO (J = 1-0) measurements are reported for 29 galaxies of intermediate IR lumionosity in the IRAS Bright Galaxy sample, at distances in the range 20-40 Mpc. Most of the galaxies were mapped at 3-7 points with a 55 arcsec beam. The total H2 masses, assuming a standard Galactic CO-to-H2 conversion ratio, lie in the range of 500 million to 20 billion solar masses. The mean ratio of L(FIR)/M(H2) for this intermediate luminosity sample is approximately three times that found for Virgo spirals and approximately one-third of that found for a sample of higher-luminosity IRAS Bright Galaxies.