This paper presents an account of English non-restrictive (`appositive') relative clauses (NRCs) in the framework of `construction based' HPSG. Specifically, it shows how the account of restrictive relative clause constructions presented in Sag (1997) can be extended to provide an account of the syntax and semantics of NRCs and of the main differences between NRCs and restrictive relatives. The analysis reconciles the semantic intuition that NRCs behave like independent clauses with their subordinate syntax. A significant point is that, in contrast with many other approaches, it employs only existing, independently motivated theoretical apparatus, and requires absolutely no new structures, features, or types.