A capsulorhexis apparatus includes a capsulorhexis probe configured for insertion into an eye through an incision and a pulse generator configured to deliver at least one radio-frequency (RF) pulse to the capsulorhexis probe. The delivered RF pulse has a pre-determined attenuation profile such that the power level of the delivered RF pulse is substantially attenuated over the RF pulse's duration. In some embodiments, the pulse generator is configured to deliver a series of two or more RF pulses to the eye, such that the energy of each of the second and subsequent pulses of the series is substantially attenuated relative to the energy of the immediately preceding pulse.