Dipolar effects in solution nuclear magnetic resonance lead to additional peaks in two-dimensional experiments. These peaks, which have the experimental properties of intermolecular multiple-quantum coherences, have been used in a variety of applications. Most efforts have focused on intermolecular zero-quantum or double-quantum coherences, which originate in two-spin terms from the equilibrium density matrix. In this paper, we characterize the "third-order experiments" (Hahn echo decay and triple-quantum CRAZED, which both originate in the three-spin terms in the equilibrium density matrix) both theoretically and experimentally. For example, in the coupled-spin picture, Hahn echo decays in concentrated solutions arise initially from intermolecular, 3-spin, -1-quantum coherences, which are partially converted to 3-spin, +1-quantum coherences by the second pulse, and hence survive the 1:1 coherence transfer echo. Such terms require two dipolar couplings to become observable. We discuss the general properties of both of these sequences, and show that they only give information that is already present in the "second-order" double-quantum and zero-quantum experiments. Finally, we also show that relaxation and diffusion can be introduced into the coupled-spin picture in a straightforward manner.