Estimation strategies in the presence of nuisance parameters

Suppose that the observed data depend both on certain parameters we want to estimate and on other parameters we do not care about. In other words, there are both wanted and unwanted parameters. Assuming that the latter are known, should we exploit this information to design good estimators for the former? From an example we work out in this paper, it appears that the answer depends on whether we restrict ourselves to unbiased estimators or, vice versa, we also allow biased estimators. Exploiting knowledge of unwanted parameters is recommended with unbiased estimators. With biased estimators, instead, this may not be the winning strategy.