  A close connection between the no-name lemma (concerning algebraic groups
acting on vector bundles) and the existence of sufficiently many independent
rational covariants is pointed out. In particular, this leads to a new natural
proof of the no-name lemma. For linearly reductive groups, the approach has a
refined variant based on integral covariants. This fits into the usual context
of invariant theory, and yields a version of the no-name lemma that has a
constructive nature.
