Laming [Laming, D. (2006). "Predicting free recalls." "Journal of Experimental Psychology: Learning, Memory, and Cognition," 32, 1146-1163] has shown that, in a free-recall experiment in which the participants rehearsed out loud, entire sequences of recalls could be predicted, to a useful degree of precision, from the prior sequences of stimuli and rehearsals. This article describes an improved predictive algorithm, which is then used to re-analyse two further sets of free-recall data. Prediction is compared, generically, with conventional modelling, represented here by three recent models of free recall that are concerned with recalls only, not with rehearsals. Some implications are drawn, from the use of rehearsal data by the predictive algorithm, for some of the constituent assumptions embodied in those three models. (Contains 7 figures and 6 tables.)