Deuterium magnetic resonance is used to study the shape and size of ribbon-like aggregates as well as the contrasting molecular ordering which is shown to occur in different regions of the aggregate. Elongated ribbon-like aggregate structures are formed from a ternary mixture of potassium palmitate/potassium laurate/water. Deuterium spectral patterns from various selectively deuterated sites of the potassium palmitate compound are analyzed in terms of a simple model for the ribbon structure. The results indicate that the order parameter S of the terminal methyl position is enhanced by a factor of 2 in the curved cylindrical edge of the ribbon over its value in the uncurved central lamellar-like region. The size of the ribbon model is also determined. At lower temperature, the ribbons transform into cylindrical aggregates on a rectangular lattice. Deuterium magnetic resonance of water is shown to be sensitive to the details of the lattice structure.