Let be a connected simple graph and let be the spectrum of integers for which there exists a -design of order . Put , with and . Denote by the graph having vertex set and edge set . Let be a -design. We say that two -designs , , are exactly embedded into if , and there is a bijective mapping such that is a subgraph of , for every . We give necessary and sufficient conditions so that two -designs can be exactly embedded into a -design. We also consider the following two problems: (1) determine the pairs for which any two nontrivial -designs , , , can be exactly embedded into a -design; (2) determine the pairs for which there exists a -design of order exactly embedding two nontrivial -designs , , . We study these problems for BIBDs, cycle systems, cube systems, path designs and star designs.