This paper discusses transmission strategies for dealing with the problem of self-interference in multi-hop wireless networks in which the nodes communicate in a fullduplex mode. An information theoretic study of the simplest such multi-hop network: the two-hop source-relay-destination network, leads to a novel transmission strategy called structured self-interference cancellation (or just "structured cancellation" for short). In the structured cancellation strategy the source restrains from transmitting on certain signal levels, and the relay structures its transmit signal such that it can learn the residual self-interference channel, and undo the selfinterference, by observing the portion of its own transmit signal that appears at the signal levels left empty by the source. It is shown that in certain nontrivial regimes, the structured cancellation strategy outperforms not only half-duplex but also full-duplex schemes in which time-orthogonal training is used for estimating the residual self-interference channel.