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Unbiased angular diameter measurements are required for accurate distances to Cepheids using the interferometric Baade-Wesselink method (IBWM). The precision of this technique is currently limited by interferometric measure-ments at the 1.5 % level. At this level, the center-to-limb darkening (CLD) and the presence of circumstellar envelopes (CSE) seem to be the two main sources of bias. The observations we performed aim at improving our knowledge of the interferometric visibility profile of Cepheids. In particular, we assess the systematic presence of CSE around Cepheids in order determine accurate distances with the IBWM free from CSE biased angular diameters. We ob-served a Cepheid (YOph) for which the pulsation is well resolved and a nonpulsating yellow supergiant ( Per) using long-baseline near-infrared interferometry. We interpreted these data using a simple CSE model we previously de-veloped.We found that our observations of Per do not provide evidence for a CSE. Themeasured CLD is explained by an hydrostatic photospheric model. Our observations of Y Oph, when compared to smaller baseline measurements, suggest that it is surrounded by a CSEwith characteristics similar to CSEs found previously around other Cepheids.We have determined the distance to Y Oph to be d 491 18 pc. Additional evidence points toward the conclusion that most Cepheids are surrounded by faint CSEs, detected by near-infrared interferometry: after observing four Cepheids, all show evidence for a CSE. Our CSE nondetection around a nonpulsating supergiant in the instability strip, Per