[en] The strong decay properties of the newly observed states D_sJ(3040), D_sJ(2860), and D_sJ(2710) are studied in a constituent quark model with quark-meson effective Lagrangians. We find that the D_sJ(3040) could be identified as the low-mass physical state |2P₁>_L (J^P=1⁺) from the D_s(2¹P₁)-D_s(2³P₁) mixing. The D_sJ(2710) is likely to be the low-mass mixed state |(SD)>_L via the 1³D₁-2³S₁ mixing. In our model, the D_sJ(2860) cannot be assigned to any single state with a narrow width and compatible partial widths to DK and D*K. Thus, we investigate a two-state scenario as proposed in the literature. In our model, one resonance is likely to be the 1³D₃ (J^P=3^-), which mainly decays into DK. The other resonance seems to be the |1D₂^'>_H, i.e. the high-mass state in the 1¹D₂-1³D₂ mixing with J^P=2^-, of which the D*K channel is its key decay mode. We also discuss implications arising from these assignments and give predictions for their partner states such as |(SD)^'>_H, |2P₁^'>_H, 2³P₀, and 2³P₂, which could be helpful for the search for these new states in future experiments.