We show the possible existence of compact stars having a surface composed of a mixed phase of quarks and hadrons. This scenario can be realized both for self-bound stars, satisfying the so-called Witten-Bodmer hypothesis, and for gravitationally bound stars. Recently several analysis of observational data have emphasized the possible existence of compact stars having very small radii, of the order of 9 kilometers or less [1]. To account theoretically for the existence of such a star, one would need to use of very soft Equations of State (EOSs), that can be obtained, in principle, introducing kaon condensation [2-4], or hyperonic degrees of freedom [5][6][7]. Another possibility is to consider quark stars, where the density of the surface is above nuclear matter saturation density. These objects have been obtained till now assuming the validity of the hypothesis introduced independently by Bodmer [8] and Witten [9], which states that the true and absolute ground state of the strong interaction is a state of deconfined quark matter. The latter consists of an approximately equal number of up, down and strange quarks having energy per baryon E/A smaller than that of iron (E F e ≈ 930 MeV), at zero temperature and pressure [10]. Stars entirely composed of matter in such ultra-stable state are self-bound [11,12] and could rotate with a period well below one millisecond [13,14].A possible problem in interpreting neutron stars as strange quark stars is the difficulty of having glitches in the latter, since the most widely accepted model for the glitches require the existence of a crystallized phase trapping magnetic