A narrow plane cut near the crystal surface increases the probability of capture into the stable channeling motion up to 99 percent

It is shown that a narrow plane cut near the crystal surface considerably increases the probability of capture into the stable channeling motion of positively charged particles entering a crystal at angles smaller than a quarter of the critical channeling angle with respect to the crystal planes. At smallest incidence angles the capture probability reaches 99 percent. A pair of crystals with cuts bent in orthogonal planes allows to reach a 99.9 percent efficiency of single-pass deflection of a proton beam with an ultra small divergence. Conditions necessary for efficient single-pass deflection of protons from the LHC beam halo are discussed.