Let k be a field, let G be a linear algebraic group over k and let V be a generically free linear representation of G. Noether's problem consists in determining whether the (birational) quotient V/G is stably rational over $k$. The answer does not depend on the choice of V, thanks to the well-known 'no-name lemma'. In this talk, we consider the following question. Assume Noether's problem for G has a positive answer. Given a generically free representation V of G, is the birational quotient V/G -rational- over k? To my knowledge, there is no known counterexample to this question. We shall focus on particular cases where G is a rational variety and a special group- in which case, of course, Noether's problem has a positive answer. This is joint work with Michel Van Garrel.