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From detailed numerical calculations, we demonstrate that in simple photonic crystal structures, a discrete number of Bloch surface-localized eigenstates can exist inside the continuum of free-space modes. Coupling to the free space causes the surface modes to leak, but the forward and back-reflected leakage may interfere destructively to create a perfectly bound surface state with zero leakage. We perform analytical temporal coupled-mode theory analysis to show the generality of such phenomenon and its robustness from variations of system parameters. Periodicity, time-reversal invariance, two-fold rotational symmetry and a perfectly reflecting boundary are necessary for these unique states. Inside the periodic structure of a photonic crystal, photons behave analogously to electrons in solid-state materials. Localized light patterns can be found at the interface between a photonic crystal and the surrounding air. Such surface states can exist even when the light has a possibility of escaping into the air, as Marin Soljačić and co-workers at the Massachusetts Institute of Technology and Harvard University, USA, now show in a theoretical study. They demonstrate that under certain conditions, different leakage channels from the crystal surface interfere destructively and thus cancel each other completely. These findings should help in the design of photonic-crystal structures for applications such as sensing and spectroscopy, where strongly localized light states are desired.