We consider localization of gravity on thick branes with a nontrivial structure. Double walls that generalize the thick Randall-Sundrum solution, and asymmetric walls that arise from a ${Z}_{2}$ symmetric scalar potential, are considered. We present a new asymmetric solution: a thick brane interpolating between two ${\mathrm{A}\mathrm{d}\mathrm{S}}_{5}$ spacetimes with different cosmological constants, which can be derived from a ``fake supergravity'' superpotential, and show that it is possible to confine gravity on such branes.