On compact exceptional objects in derived module categories

Let A   be a basic and connected finite dimensional algebra and Db(A)Db(A) be the bounded derived category of finitely generated left A  -modules. In this paper we consider lengths of tilting objects and indecomposable compact exceptional objects in Db(A)Db(A), and prove 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 criterion are bounded derived simple, and describe an algorithm to construct a family of algebras satisfying this condition.