In the framework of spin-0 s-channel dark matter (DM) simplified models, we reassess the sensitivity of future LHC runs to the production of DM in association with top quarks. We consider two different missing transverse energy (E miss T ) signatures, namely production of DM in association with either a tt pair or a top quark and a W boson, where the latter channel has not been the focus of a dedicated analysis prior to this work. Final states with two leptons are studied and a realistic analysis strategy is developed that simultaneously takes into account both channels. Compared to other existing search strategies the proposed combination of tt + E miss T and tW + E miss T production provides a significantly improved coverage of the parameter space of spin-0 s-channel DM simplified models. reach of tt + E miss T analyses (see very recently also [12,13]). The work [14] has then shown that a dedicated search for t-channel t j + E miss T production can provide an interesting stand-alone DM signal at the LHC. Both of these studies have been performed in the context of spin-0 s-channel DM simplified models. The article [15] has finally studied single-top plus E miss T production in an ultraviolet (UV) complete model with two Higgs doublets (2HDM) and an extra pseudoscalar mediator, known as the 2HDM+a model [16][17][18][19][20][21]. In the framework of the 2HDM+a model it has been shown that tW + E miss T is the most interesting channel because it can be resonantly procedure via the exchange of a charged Higgs boson. A dedicated analysis of the tW + E miss T final state in spin-0 s-channel DM simplified models has instead not been performed so far. The main goal of this work is to close this gap by developing an analysis which provides an improved coverage of the parameter space of spin-0 s-channel DM simplified models via a combined two-lepton search for tt + E miss T and tW + E miss T production. The outline of this article is as follows. In Section 2 we describe the structure of the DM simplified models that we consider. Section 3 contains a discussion of unitarity violation in DM plus top-quark production. From this discussion one can conclude that calculations of the tW+E miss T signature in the context of spin-0 s-channel DM simplified models lead to meaningful results at LHC energies. The angular correlations of the tW + E miss T signal are discussed in Section 4, while a brief description of our Monte Carlo (MC) and detector simulations is presented in Section 5. Our actual analysis strategy can be found in Section 6. It spells out all selection criteria and illustrates their impact on the DM signals and the SM background. In Section 7, we present the numerical results of our analysis, providing a detailed evaluation of the achievable sensitivity of tt + E miss T and tW + E miss T production at future LHC runs. Constraints on the parameter space of the spin-0 s-channel DM simplified models are also derived in this section. We conclude in Section 8.