New CO observations of a complete sample of starburst galaxies are presented in order to determine the range of molecular gas masses and star-formation efficiencies that characterize these systems. The properties of the galaxies in the sample are given, and the H-alpha and R-band CCD images for six of the galaxies are shown. The novel feature of this study is that the galaxies in this study are infrared selected as opposed to optically selected. They exhibit levels of nuclear star formation activity which are comparable to the starburst galaxies M82 and NGC 253. A subset of galaxies with unusually narrow CO line widths, high star-formation efficiencies, and compact 10-micron distributions is revealed. It is proposed that, if gas distributions in these galaxies are also compact, as the narrow linewidths suggest, the high yields of massive stars per unit mass of molecular gas may be attributed to a star-formation mechanism which becomes more efficient as the gas density increases.