This article presents a typed feature structure grammar formalism for Mainland Scandinavian which outperforms existing grammars in several respects: it is multilingual and captures dialectal variation and many typological facts, and it is computationally efficient. Our reference point is the grammar formalism of Underwood (1997). It is proven that Underwood's formalism is intractable. Our formalism improves on this result, i.e. it is decidable in polynomial time. The article covers the phenomena covered in Underwood (1997) and non-local dependencies.