The recent remark by Mourou and Tajima, Science 331, 41 (2011), on the intensity of the driver laser pulse and the duration of the created pulse that higher driver beam intensities are needed to reach shorter pulses of radiation remains a conjecture without clear theoretical reasoning so far. Here we discuss the observations leading to the conjecture and offer its extension to the case of relativistic electron bunches as the laser's radiating medium (free-electron laser). The idea is further extended towards the regime of vacuum non-linearities.