  Let $A$ be a finite dimensional algebra and $D^b(A)$ be the bounded derived
category of finitely generated left $A$-modules. In this paper we consider
lengths of compact exceptional objects in $D^b(A)$, proving a sufficient
condition such that these lengths are bounded by the number of isomorphism
classes of simple $A$-modules. Moreover, we show that algebras satisfying this
condition is bounded derived simple.
