  The strong decays of $D^\star_{s1}(2700)^\pm$ and $D^\star_{sJ}(2860)^\pm$
are investigated within the $^3P_0$ model. It is found that the interpretation
of these two states depends on the mixing schemes and the ways of choices of
the harmonic oscillator parameter $\beta$. If $D^\star_{s1}(2700)^\pm$ and
$D^\star_{sJ}(2860)^\pm$ are two pure states, $D^\star_{s1}(2700)^\pm$ seems
impossibly the $2^3S_1$ $D_s$, but may be the $1^3D_1$ $D_s$.
$D^\star_{sJ}(2860)^\pm$ may be the $1^3D_3$. If there is mixing between the
$2^3S_1$ and $1^3D_1$, $D^\star_{s1}(2700)^\pm$ may be the mixed $1^-$ state
with a small mixing angle in the case of a special $\beta$ for each meson, and
$D^\star_{sJ}(2860)^\pm$ is the orthogonal partner of $D^\star_{s1}(2700)^\pm$;
$D^\star_{s1}(2700)^\pm$ may also be the mixed $1^-$ state with a large mixing
angle based on a universal $\beta$ for all mesons, and $D^\star_{sJ}(2860)^\pm$
seems impossibly the orthogonal partner of $D^\star_{s1}(2700)^\pm$. Other
uncertainties related to the choices of constituent quark masses and phase
spaces are also explored.
