In this paper we introduce and study credibility-limited improvement operators. The idea is to accept the new piece of information if this information is judged credible by the agent, so in this case a revision is performed. When the new piece of information is not credible then it is not accepted (no revision is performed), but its plausibility is still improved in the epistemic state of the agent, similarly to what is done by improvement operators. We use a generalized definition of Darwiche and Pearl epistemic states, where to each epistemic state can be associated, in addition to the set of accepted formulas (beliefs), a set of credible formulas. We provide a syntactic and semantic characterization of these operators.