A method that allows estimating consensus trees without exhaustive searches is described. The method consists of comparing the results of different independent superficial searches. The results of the searches are then summarized through a majority rule, consensed with the strict consensus tree of the best trees found overall. This assumes that to the extent that a group is recovered by most searches, it is more likely to be actually supported by the data. The effect of different parameters on the accuracy and reliability of the results is discussed. Increasing the cutoff frequency decreases the number of spurious groups, although it also decreases the number of correct nodes recovered. Collapsing trees during swapping reduces the number of spurious groups without significantly decreasing the number of correct nodes recovered. A way to collapse branches considering suboptimal trees is described, which can be extended as a measure of relative support for groups; the relative support is based on the Bremer support, but takes into account relative amounts of favorable and contradictory evidence. More exhaustive searches increase the number of correct nodes recovered, but leave unaffected (or increase) the number of spurious groups. Within some limits, the number of replications does not strongly affect the accuracy of the results, so that using relatively small numbers of replications normally suffices to produce a reliable estimation.