Abstract.A powerful method for the analysis of the structure of small scale magnetic elements in the solar photosphere is the inversion of Stokes spectra. In previous papers based on such inversions Bellot Rubio et al. (1997Rubio et al. ( , 1999 and Frutiger et al. (1999) have argued in favor of models with rather different dynamic properties. In this paper we return to this debate and compare results returned by inversions based on new multi-component models applied to several Fe i, Fe ii and C i spectral line profiles obtained in active region plage with a Fourier Transform Spectrometer. These inversions differ from earlier ones by the fact that mass conservation is strictly imposed both inside the magnetic elements and on the surrounding external flow field. These flux-tube models are not only able to reproduce the characteristic Stokes V asymmetries and line-shifts observed in active regions plages or network elements, but also the Stokes I line profiles, including line bisectors. It is confirmed that from the quality of the fits alone it is not possible to distinguish between the steady flow proposed by Bellot Rubio et al. (1997) and the oscillatory model of Frutiger & Solanki (1998). If, however, physical constraints are imposed (e.g. mass conservation or that the flow retains the same direction over height in the flux tube) then the oscillatory model is found to be superior. In addition, the current investigation also provides the first inversion-based model of abnormal granulation.