The diametral dimension of a nuclear Fréchet space E, which satisfies ( DN) and (Ω), is related to power series spaces Λ(ε) and Λ(ε) for some exponent sequence ε. It is proved that E contains a complemented copy of Λ(ε) provided the diametral dimensions of E and Λ(ε) are equal and ε is stable. Assuming Λ(ε) is nuclear, any subspace of Λ(ε) which satisfies ( DN), can be imbedded into E. Applications of these results to spaces of analytic functions are given.