Cyclic peptides have the potential to bind to challenging targets, which are undruggable with small molecules, but their application is limited by low membrane permeability. Here, using a series of cyclic pentapeptides, we showed that established physicochemical criteria of permeable peptides are heavily violated. We revealed that a dominant core conformation, stabilized by amides' shielding pattern, could guide the design of novel compounds. As a result, counter-intuitive strategies, such as incorporation of polar residues, can be beneficial for permeability. We further find that core globularity is a promising descriptor, which can extend the capability of standard predictive models.