An ophthalmic surgical laser system includes: a laser that produces a pulsed laser beam having a pulse energy and pulse repetition rate; a high frequency fast scanner; an XY-scan device; a Z-scan device; and a controller. The controller controls the high frequency scanner to produce a scan line having a scan width; controls the XY-scan device and the Z-scan device to carry out of first sweep of the scan line in a first sweep direction and to carry out a second sweep of the scan line in a second sweep direction that is not parallel to the first sweep direction thereby defining an overlap region. At least one of the pulse energy, repetition rate, XY-scan speed, and the scan width is varied so as to accelerate the cutting speed and reduce the exposure of ophthalmic tissue in the overlap region to multiple exposures of laser pulses configured to modify ophthalmic tissue.