The evidence of the presence of staggering in TX-100 and the conflicting data in the literature regarding the micelle shape make this system an excellent candidate for exploring the use of data-driven simulations to investigate these assemblies beyond the core-shell model. We used SAXS and SANS experiments and Metainference simulations to study TX-100 and C12EO10 (Figure , inset), showing how going beyond core-shell models may be necessary when modelling surfactants. C12EO10 and TX-100 have similar molecular weights and hydrophilic EO chains, differing only in the hydrophobic moiety. Although the structure of the C12EO10 micelles can be described relatively well with regular core-shell models, the same is not true for TX-100, where our attempts to simultaneously fit a single model for both SAXS and SANS data were unsuccessful. We show that, in line with what has been previously suggested, the reason is the diffuse boundaries between the hydrophobic and hydrophilic regions as well as the presence of non-trivial multidomain structures and even toroidal assemblies.