  We present exact expressions for elementary boundary states which describe
D-branes preserving 16 or fewer supercharges in type II superstring
compactified on certain self-dual 4-tori. While being manifestly
superconformal, our boundary states are not a priori required to satisfy the
usual free-field gluing conditions along the internal directions of the 4-tori.
Our calculations proceed along the lines of Gepner's construction by recasting
the $\mathcal{N}=(2,2)$ worldsheet sigma model on the 4-tori in terms of
$\mathcal{N}=2$ minimal models. Imposing general permutation gluing conditions
on the $\mathcal{N}=(2,2)$ generators is shown to yield various stable and
unstable D-branes, where the stable ones include the known 1/2-BPS and 1/4-BPS
bound states of D$p$-branes, as well as new non-BPS D-branes, which do not
carry RR charges.
