Summary: We examine the computably enumerable (c.e.) degrees of prime models of complete atomic decidable (CAD) theories. A structure has degree \(\mathbf d\) if \(\mathbf d\) is the degree of its elementary diagram. We show that if a CAD theory \(T\) has a prime model of c.e. degree \(\mathbf c\), then \(T\) has a prime model of strictly lower c.e. degree \(\mathbf b\), where, in addition, \(\mathbf b\) is low (\(\mathbf b^\prime =\mathbf 0^\prime \)). This extends Csima’s result that every CAD theory has a low prime model. We also prove a density result for c.e. degrees of prime models. In particular, if \(\mathbf c\) and \(\mathbf d\) are c.e. degrees with \(\mathbf d < \mathbf c\) and \(\mathbf c\) not low\(_2\) \((\mathbf c^{\prime \prime } > \mathbf 0^{\prime \prime})\), then for any CAD theory \(T\), there exists a c.e. degree \(\mathbf b\) with \(\mathbf d < \mathbf b < \mathbf c\) such that \(T\) has a prime model of degree \(\mathbf b\), where \(\mathbf b\) can be chosen so that \(\mathbf b^\prime\) is any degree c.e. in \(\mathbf c\) with \(\mathbf d^\prime \leq \mathbf b^\prime \). As a corollary, we show that for any degree \(\mathbf c\) with \(\mathbf 0 <\mathbf c <\mathbf 0^\prime\), every CAD theory has a prime model of low c.e. degree incomparable with \(\mathbf c\). We show also that every CAD theory has prime models of low c.e. degree that form a minimal pair, extending another result of Csima. We then discuss how these results apply to homogeneous models.