The neighborhood of 745 luminous stars in the IRAS Skyflux plates was examined for the presence of dust heated by the nearby star. One-hundred twenty-three dust clouds were found around only 106 of the stars with a volume filling factor of 0.006 and an intercloud separation of 46 pc. Nowhere was a region found where the dust is smoothly distributed through the volume of space heated by the star; hence an upper limit of 0.06/cu cm is placed on the equivalent gas density in the intercloud regions. Due to the lack of IR emission near the star, it is found that less than 1 percent of the stellar luminosity is reprocessed within 10 pc of the star. The clouds have an average density of 0.22/cu cm and a radius of 1.9 pc, albeit with wide variations in their properties. Two different scale heights of 140 and 540 pc were found for the number of clouds around different groups of stars, which are interpreted as evidence for different distributions of dust in and out of the Galactic disk.