Obtaining high signal levels in fluorescence microscopy is usually spoiled by the concomitant population of the dark (triplet) state of the marker, which is often followed by photobleaching. Recently, we introduced the triplet relaxation (T-Rex) modality in fluorescence microscopy which led to a major increase in total signal and dye photostability. The idea behind T-Rex is to avoid the illumination of fluorophores in the triplet state, e.g. by using pulsed excitation with interpulse time distances that are long enough for the triplet state to relax between two pulses. While our previous implementation came at the expense of extended recording, here we investigate pulsed excitation patterns for T-Rex illumination implying shorter total recording times. In particular, we balance signal enhancement and imaging speed by exciting with bunches of quickly succeeding pulses that are separated by dark periods for triplet relaxation. Taking the green fluorescent protein and the organic dye Atto532 as examples, we observe the dependence of photobleaching and total fluorescence gain on the number of pulses within a bunch. Reaching almost T-Rex conditions this excitation scheme mimics fast scanning of the illumination beam and has the potential to improve a whole range of analytical tools that suffer from photobleaching and low signal levels.