Confidence limits: what is the problem? Is there the solution?

This contribution to the debate on confidence limits focuses mostly on thecase of measurements with `open likelihood', in the sense that it is defined inthe text. I will show that, though a prior-free assessment of {\it confidence}is, in general, not possible, still a search result can be reported in a mostlyunbiased and efficient way, which satisfies some desiderata which I believe areshared by the people interested in the subject. The simpler case of `closedlikelihood' will also be treated, and I will discuss why a uniform prior on asensible quantity is a very reasonable choice for most applications. In bothcases, I think that much clarity will be achieved if we remove from scientificparlance the misleading expressions `confidence intervals' and `confidence levels'.