The peculiar F-type supergiant HD 101584, which has a large and unusual infrared excess, is discussed along with the possibility that the infrared radiation could be accounted for by a cool companion. The peculiar F supergiants 89 Her, v Sgr, and R CrB are also considered as possible binary systems containing an infrared star. It is pointed out that all four of these stars have infrared excesses with characteristics similar to the infrared radiation from several cool objects which are known single stars.