  We generalise the techniques of semistable reduction for flat families of
sheaves to the setting of the derived category $D^b(X)$ of coherent sheaves on
a smooth projective three-fold $X$. Then we construct the moduli of
PT-semistable objects in $D^b(X)$ as an Artin stack of finite type that is
universally closed. In the absence of strictly semistable objects, we construct
the moduli as a proper algebraic space of finite type.
