Consensus methods can be used for reconstructing a species tree from several gene trees, which exhibit incompatible topologies due to incomplete lineage sorting. Motivated by the fact that there are no anomalous rooted gene trees with three taxa and no anomalous unrooted gene trees with four taxa in the multispecies coalescent model, several contemporary methods form the gene tree consensus by finding the median tree with respect to the triplet or quartet distance-i.e. estimate the species tree as the tree which minimizes the sum of triplet or quartet distances to the input gene trees. These methods reformulate the solution to the consensus problem as the solution to a recursively solved dynamic programming (DP) problem. We present an iterative, easily parallelizable approach to finding the exact median triplet tree and implement it as an open source software package that can also find suboptimal consensus trees within a specified triplet distance to the gene trees. The most time-consuming step for methods of this type is the creation of a weights array for all possible subtree bipartitions. By grouping the relevant calculations and array update operations of different bipartitions of the same subtree together, this implementation finds the exact median tree of many gene trees faster than comparable methods, has better scaling properties with respect to the number of gene trees and has a smaller memory footprint.;RTIST (Rooted Triple Inference of Species Trees) finds the exact median triplet tree of a set of gene trees. Its runtime and memory footprints scale better than existing algorithms. RTIST can resolve all the non-unique median trees, as well as sub-optimal consensus trees within a user-specified triplet distance to the median. Although it is limited in the number of taxa (≤20), its runtime changes little when the number of gene trees is changed by several orders of magnitude.;RTIST is written in C and Python. It is freely available at https://github.com/glebzhelezov/rtist.