There are currently several commercially available radiotherapy treatment units without a flattening filter in the beam line. Unflattened photon beams have an energy and lateral fluence distribution that is different from conventional beams and, thus, their attenuation properties differ. As a consequence, for flattening filter free (FFF) beams, the relationship between the beam-quality specifier TPR20,10 and the Spencer-Attix restricted water-to-air mass collision stopping-power ratios, L̄/ρair (water), may have to be refined in order to be used with equivalent accuracy as for beams with a flattening filter. The purpose of this work was twofold. First, to study the relationship between TPR20,10 and L̄/ρair (water) for FFF beams, where the flattening filter has been replaced by a metal plate as in most clinical FFF beams. Second, to investigate the potential of increasing the accuracy in determining L̄/ρair (water) by adding another beam-quality metric, TPR10,5. The relationship between L̄/ρair (water) and %dd(10)x for beams with and without a flattening filter was also included in this study.