We report point-contact measurements in high-quality single crystals of Cu_0.2Bi₂Se₃. We observe three different kinds of spectra: (1) Andreev-reflection spectra, from which we infer a superconducting gap size of 0.6 mV; (2) spectra with a large gap which closes above T_c at about 10 K; and (3) tunnelinglike spectra with zero-bias conductance peaks. These tunneling spectra show a very large gap of ∼2 meV (2Δ/K_bT_c ∼14).