The Owens Valley millimeter-wave interferometer has been used for high-resolution (approximately 3"-7") mapping of the CO emission in three luminous IRAS galaxies: IRAS 17208-0014, Zw 049.057 (IRAS 15107 + 0724), and IRAS 10173 + 0828. These galaxies are among the most extreme, in terms of their L(ir)/L(B) ratio [= nu-F-nu(80-mu-m)/nu-f-nu(0.44-mu-m)], for objects in the IRAS Bright Galaxy Surveys (Soifer et al. 1987, 1989; Sanders et al. 1990). The CO emission detected in the three galaxies originates from a single region centered on the IRAS emission peak. Practically all the molecular gas in IRAS 17208-0014 has been detected with the interferometer; a molecular mass of 5.5 x 10(10) M. is located in a 1.2 kpc radius region centered on the infrared nucleus of this galaxy. Roughly all the molecular gas (approximately 4 x 10(9) M.) in the galaxy Zw 049.057 is located at less than 0.37 kpc from the nucleus. Lower resolution observations of IRAS 10173 + 0828 are only sufficient to show that approximately half (9 x 10(9) M.) of the total mass of H-2 gas is located at less than 3.2 kpc from the nucleus. Although the infrared luminosity of IRAS 17208-0014 and Zw 049.057 differ by one order of magnitude, our observations have shown that these galaxies have similar values for the global L(ir)/M(H-2) ratio, for the surface density of molecular gas in their central regions (approximately 10(4) M. pc-2) and for the extinction toward the nucleus (> 300 mag). Therefore, an extreme infrared luminosity may not be required to find a very high concentration of molecular gas in the nucleus of a galaxy. Instead, a high L(ir)/L(B) ratio seems to be a good predictor for both a high global L(ir)/M(H-2) ratio and very large central H-2 surface densities.