There is some confusion in the literature regarding the derived category of an exact category 8. Thomason gives a satisfactory treatment of the bounded derived category in CT, 1.11.6 (see also Appendix A)]. The result is that provided all weakly split epimorphisms in 8 are admissible, the bounded derived category may be defined as usual. Although Thomason does not say it, the categories D+(6), D-(d) may also be defined in the same way. The definition of the unbounded derived category is more difficult, and is very poorly treated in the literature. For instance, in [BBD] this derived category is only defined provided every morphism in 6 admits a kernel. (See [BBD, 1.1.41; this is very unsatisfactory since very few exact categories satisfy the condition.) In this article we will show that D(B) may be defined whenever 6 is saturated (“Karoubian” in Thomason’s terminology). An exact category is saturated if every idempotent splits; i.e., 6 contains all direct summands of its objects. For the purpose of comparing with Thomason’s result, the bounded derived category is defined for more 8’s. All that is required to define Db(&) is that whenever an idempotent e: A + A factors as A f, BA A with fog=lB, then e is split. Thomason calls such idempotents weakly split, and we will honor his notation. We will show here that these constructions are in some sense best possible (Remark 1.8 for D(6), Remarks 1.9 and 1.10 for D+(d), D-(b), Db(6)). There are two reasons why I wrote this note. One is to correct the misconceptions in the literature. But, more importantly, the proof of the key result, Lemma 1.2, depends on an important characterization of tpaisse subcategories due to Rickard, and this article is intended to highlight Rickard’s criterion: a full triangulated subcategory Y of a triangulated