The question of variance reduction within the source-iteration scheme of a Monte Carlo eigenvalue calculation is tackled. The trade-off point between improving the statistics of a local response whilst simultaneously not damaging excessively the fundamental mode, the source for the calculation of the local response in the next fission cycle, is found. It is realized that applying less normalizations, i.e. employing superhistories, is advantageous. Realistic test problems, both fast and thermal fission, with in- and ex-core local responses, are treated. There is a good agreement between the predicted and actual gain in efficiency. A single comparison with the classic formalism, based purely on shows large differences. © 2014 Elsevier Ltd. All rights reserved.