The performance characterization of decentralized wireless networks with uncoordinated sender-destination pairs motivates the study of the totally asynchronous interference channel with single-user receivers. Since this channel is not information stable, its capacity region is determined resorting to information density, although more amenable single-letter inner and outer bounds are provided as well. Aiming at numerical evaluation of the achievable rates, we subsequently concentrate on the inner bound for the Gaussian case. We show that taking Gaussian inputs is not the best choice in general and derive analytical conditions under which other input distributions may be optimal. Essentially, these conditions require the channel to be interference-limited. Finally, the existence of such non-Gaussian distributions with superior performance is validated numerically in different scenarios.