This chapter presents a simple but realistic history-matching case for a model of reservoir named REEK that we use to illustrate the crucial properties of the history-matching problem when conditioning on production rates. We start with a standard HM procedure computing global updates and demonstrating how we improve the results when properly accounting for uncertainties in model controls, dependency of measurement errors, and introducing localization schemes to reduce the impact of the spuriousSpuriouscorrelations correlations appearing when using a limited sample size. We run multiple experiments and demonstrate correlation-based Localizationcorrelation based adaptive localization for the history-matchingHistory matching update. The history-matching problem is inherently under-determined because many different parameter updates give an equally good fit to the data. The final algorithm solves for the minimum geologically consistent update of the uncertain model parameters, providing a good fit to the data.