In this paper, as a continuation of our previous work, we systematically study the mass spectra and OZI-allowed strong decays of the higher 3S-, 2P-, 2D-, and 1F-wave charmed and charmed-strange mesons within a unified unquenched quark model. It is found that for most of the higher excitations, the masses are significantly shifted down by the coupled-channel effects. The newly observed Ds1(2933)+
Nearby in the stack
reported by the LHCb collaboration could be identified as the low-mass axial-vector state
Ds(2P1)
via the
21P1−23P1
mixing. For the broad structure
DsJ(3040)+
observed earlier by the BABAR collaboration, the
Ds(31S0)
assignment seems to be favored over the high-mass mixed state
Ds(2P1′)
. Meanwhile, the
D(3000)0
signals observed at LHCb cannot be well understood with any
3S
,
2P
,
2D
, or
1F
assignments in the
D
-meson family. Our predicted masses and decay properties of the missing higher
D
and
Ds
mesons may provide useful information for future experimental searches.