Classical Be stars, in addition to their emission-line spectra, are associated with infrared excess which is attributable to free-free emission from ionized gas. However, a few with exceptionally large near-infrared excess, namely with J - H, and H-Ks both greater than 0.6 mag-and excess emission extending to mid- and far-infrared wavelengths-must be accounted for by thermal emission from circumstellar dust. Evolved Be stars on the verge of turning off the main sequence may condense dust in their expanding cooling envelopes. The dust particles should be very small in size, hence reprocess starlight efficiently. This is in contrast to Herbig Ae/Be stars for which the copious infrared excess arises from relatively large grains as part of the surplus star-forming materials.