Methods and apparatus for directing radiation pulses to a region wherein either a pulse or a substance in the region is adversely affected by the presence of more than a given power density therein. A laser pulse is split into a plurality of portions and each portion is directed along a path of different length to provide in rapid succession a plurality of pulses each having less than the given power density. Each pulse is caused to arrive at the region at an angle differing by at least its divergence angle from the arrival angle of every other pulse (or, if at a smaller angle from another pulse, with opposite polarization therefrom) and at a time enough later than the arrival time of the preceding pulse that the total power density in the region at any instant is less than the given power density. Thus, the effective total power density of the radiation directed through the region may exceed the given power density without adversely affecting any pulse or substance in the region. Typically, the region comprises an amplifier from which each pulse emerges at an angle differing by at least its divergence angle from the emergence angle of every other pulse (or, if at a smaller angle from another pulse, with opposite polarization therefrom). Each emerging pulse is separated from the others and is directed along a path of such length as to cause it to arrive at the selected location substantially simultaneously with the other pulses (or, alternatively, at such time relative to the other pulses as to provide a predetermined effective combined pulse shape at the location).