We report on an analysis of the impact of available experimental data on hard processes in proton–lead collisions during Run I at the large hadron collider on nuclear modifications of parton distribution functions. Our analysis is restricted to the EPS09 and DSSZ global fits. The measurements that we consider comprise production of massive gauge bosons, jets, charged hadrons and pions. This is the first time a study of nuclear PDFs includes this number of different observables. The goal of the paper is twofold: (i) checking the description of the data by nPDFs, as well as the relevance of these nuclear effects, in a quantitative manner; (ii) testing the constraining power of these data in eventual global fits, for which we use the Bayesian reweighting technique. We find an overall good, even too good, description of the data, indicating that more constraining power would require a better control over the systematic uncertainties and/or the proper proton–proton reference from LHC Run II. Some of the observables, however, show sizeable tension with specific choices of proton and nuclear PDFs. We also comment on the corresponding improvements as regards the theoretical treatment.