This article investigates picosecond and sub-picosecond laser micromachining of Borofloat®33 glass and provides clear evidence that a simple modification of the laser beam scanning strategy can lead to significant improvement of machining efficiency and hence process throughput. Besides studying the impact of the fundamental laser machining parameters, such as laser fluence, pulse overlap, pulse repetition frequency (PRF), pulse duration and laser spot diameter, on the machined depth, surface roughness and material removal rate (MRR), it also compares the machining results for two different laser beam scanning strategies, called here "sequential” method (SM) and “interlaced” method (IM). By changing the scanning strategy from SM to IM, the MRR can be significantly increased because IM allows high-quality machining of the glass at higher PRF values. The experimental results show that this simple, cost-free modification allows the MRR value to be increased by more than 4 times, i.e. from 0.12 mm3/s to 0.53 mm3/s. Moreover, by using a Phantom V2512 high-speed camera, the picosecond laser micromachining process using both SM and IM was filmed. The videos show that SM leads to the accumulation of glass particles within the laser-machined area, whereas in IM the glass material is removed layer by layer which leads to the generation of “cleaner” and deeper areas. The mechanisms associated with these machining improvements are discussed.