CO(1-0) and CO(2-1) observations of pedestal emission from small regions in three of the high-latitude molecular clouds are discussed. High-sensitivity spectra show extended, low-level emission in addition to the typical narrow Gaussian emission from cold clumps. The pedestal profiles resemble the wings seen in CO and other molecules in low-luminosity molecular outflow regions. The small molecule clouds almost certainly do not contain any low-mass star formation sites. The data indicate that the pedestal emission is optically thick and that the narrow-line emission is produced by cold clumps about 0.2 pc in size and density of several thousand per cu cm. The pedestal emission is produced by gas with perhaps an order of magnitude less density. Adjacent spectra reveal that a pedestal often increases in antenna temperature until it resembles a narrow Gaussian line typical of clump emission. 52 refs.