The conventional bushy tree, while capable of solving non-Markovian models in principle, suffers from a severe practical limitation: its computation time grows exponentially as the number of tree time steps increases. In this paper, the authors present a novel multifactor nonexploding bushy tree technique which breaks the computation time barrier of the conventional bushy tree and allows over 100 tree steps. A nonexploding bushy tree essentially is a subsampling of a conventional bushy tree with a significantly reduced number of tree nodes, but with no state bundling and stratification. A three-factor Brace-Gatarek-Musiela (BGM/J) LIBOR market model has been implemented with the nonexploding bushy tree technique according to an estimated market correlation, and accurate results have been obtained for caps/floors. For European and Bermudan swaptions, results comparable with those of other techniques have also been obtained. The effects of the number of factors (up to five) on the Bermudan swaption prices have been obtained through preliminary analyses. Sufficient conditions for convergence are also provided.