In the universal framework of simplified t-channel dark matter models, the calculation of the relic abundance can be dominated by mediator annihilation when the dark matter and mediator masses are almost degenerate. We analyze four representative models with scalar and fermionic mediators, confront them with direct detection limits and highlight the differences and common features between them. The mediator annihilations are considerably enhanced by the Sommerfeld effect and bound state formation. Albeit their effect is subdominant in the coannihilation regime, excited bound state levels are included as well. We find that Sommerfeld and bound-state effects can lead to $𝒪(1)$ corrections to the constraints on the DM mass in the coannihilating regime, with the precise magnitude depending on the specific model realization. In addition we provide SE+BSF4DM, an intuitive and easy to use add-on to micrOMEGAs, allowing for an automated inclusion of these effects for a generic t-channel Dark Matter Model, which is publicly available on Github.