It has been demonstrated without doubt in the literature, including elsewhere in this issue, that much better conformal dose distributions in radiation therapy can be obtained with proton beams than with photons (X-rays) or electrons. It is also clear that this remains entirely true--for the fundamental reason of particle range--even after the latest and projected developments in computer-generated IMRT (intensity-modulated radiation therapy) photon dose escalation are fully considered. We consider several examples of tumour dose-response curves that illustrate the quite large gains to be obtained when dose escalation can be achieved, if normal tissue complications can also be avoided. Two contrasting types of tumour are considered in detail, prostate tumours and non-small-cell lung carcinomas. There is a considerable way to go yet to achieve really high non-recurrence rates, especially in the lung tumours. Proton beams would make this progress much safer and more effective than any variants with photons.