Two charm-strange mesons, the Ds1*(2710) and the DsJ*(2860), have recently been observed by several experiments. There has been speculation in the literature that the Ds1*(2710) is the 2S13(cs̄) state and the DsJ*(2860) is the 1D13(cs̄) state. In this paper we explore this and other explanations in the context of the relativized quark model and the pseudoscalar emission decay model. We conclude that the Ds1*(2710) is most likely the 1D13(cs̄) state and the DsJ*(2860) is most likely the 1D33(cs̄) state with the 1D2 resonances also contributing to the observed signals and explaining the observed ratios of branching ratios to D*K and DK final states. We point out that measuring the DsJ*(2860) spin can support or eliminate this explanation and that there are six excited Ds states in this mass region: the 2S13, 2S01, 1D13, 1D33 and two 1D2 states. Observing some of the missing states would help confirm the nature of the Ds1*(2710) and DsJ*(2860) states.