On the derived dimension of abelian categories

We give an upper bound on the dimension of the bounded derived category of an abelian category. We show that if $\text{CX}$ is a sufficiently nice subcategory of an abelian category, then derived dimension of $\text{CA}$ is at most $\text{CX}$-dim$\text{CA}$, provided $\text{CX}$-dim$\text{CA}$ is greater than one. We provide some applications.