Consider an additive Gaussian noise channel affected by an additive interference sequence, taken from a given codebook, which is known non-causally at the transmitter (e.g., via prior decoding). It is known that in this case optimal performance is attained by Dirty Paper Coding, which treats the interference signal as unstructured. In other words, for this example, the knowledge of the specific interferer's codebook at the decoder is not useful in terms of capacity. In this paper, two variations of this basic scenario are presented in which treating interference as unstructured is instead generally suboptimal. In the first case, a second encoder of the source message is present in the system that is not aware of the interferer's sequence, and source and interference messages are uncorrelated; In the second case, the sources encoded by the informed transmitter and interferer are correlated (and an uninformed encoder may or may not be present). Results are given in terms of conditions for achievability for both discrete and Gaussian models of the scenarios discussed above, and corroborated by numerical results. Optimal strategies are also identified in special cases. The conclusions herein point to the importance of exploiting the interfererence structure in multiterminal and source-channel coding scenarios.