We report on an experimental study of the performance of a lead/scintillating-fiber calorimeter intended for the detection of leptons, hadrons, gammas and missing energy. In particular, the effects of reducing the charge collection time down to values that are relevant for experiments at the future proton-proton colliders LHC and SSC are investigated. The total calorimeter signal, the energy resolution, the e/π signal ratio, the signal linearity, the hadronic shower profile and the electron/pion separation capability of the detector are measured as a function of the charge collection time, ranging from 5 to 358 ns. The performance is practically unaffected down to ∼40 ns, even when unrealistically long signal cables are used and no signal shaping is applied. For shorter gates, we observe incomplete charge collection, a gradually deteriorating energy resolution, an increase in the e/π signal ratio and in the hadronic signal nonlinearity, a narrowing of the hadronic shower profile and a degradation of the electron/pion separation. However, even for gates as short as the LHC/SSC bunch-bunch spacing (∼ 15 ns), these effects are not unacceptably large. The experiments were performed in the framework of the LAA project at CERN.