Let $R$ be a commutative Noetherian local ring and let $D(R)$ be the derived category of $R$-modules. Recall that a chain complex $C_\bullet$ of modules over $R$ is called perfect if it is isomorphic in $D(A)$ to a bounded complex of free and finitely generated $R$-modules. My question is this: is the category of perfect complexes with finite length homology a thick subcategory of $D(A)$? Actually I only need it to be triangulated. So if the answer to the previous question is negative, then I would like to know if the category of perfect complexes with finite length homology is a triangulated subcategory of $D(A)$? Any references for these will be appreciated.