  By computing reducibility points of parabolically induced representations, we
construct, to within at most two unramified quadratic characters, the Langlands
parameter of an arbitrary depth zero irreducible cuspidal representation $\pi$
of a classical group (which may be not-quasi-split) over a nonarchimedean local
field of odd residual characteristic. From this, we can explicitly describe all
the irreducible cuspidal representations in the union of one, two, or four
L-packets, containing $\pi$. These results generalize the work of
DeBacker-Reeder (in the case of classical groups) from regular to arbitrary
tame Langlands parameters.
