The Dependent Object Types (DOT) family of calculi has been proposed as theoretic foundation for Scala and similar languages, unifying functional programming, object oriented programming and ML-style module systems. Following the recent type soundness proof for DOT, the present paper aims to establish stronger metatheoretic properties. The main result is a fully mechanized proof of strong normalization for D$_{<:>}$, a variant of DOT that excludes recursive functions and recursive types. We further discuss techniques and challenges for adding recursive self types while maintaining strong normalization, and demonstrate that restricted variants of recursive self types can be integrated successfully.