We investigated the structures formed in water by small triblock copolymers consisting of two poly(ethylene oxide) (PEO) side blocks and a central poly(dimethylsiloxane) (PDMS) block. Our objective was to identify a possible relation between the spontaneous curvature of copolymers and their efficiency in the demulsification of water-in-crude oil emulsions observed in earlier studies. Spherical micelles containing about 100 molecules, i.e., with a highly curved structure, were detected using concentrations of up to 20 wt % of copolymer in water at room temperature. At higher concentrations or at higher temperature, micelles changed to an elongated shape. SAXS data and analysis of electron density profile variation inside the scattering object revealed the inner structure of the micelle. Finally, the role of the high spontaneous curvature of the demulsifier copolymer is discussed in relation with the mechanism of coalescence of water droplets involved in the breaking of water-in-crude oil emulsions.