Methods for the preparation of narrow-distribution ROMP polycyclopentene are developed to suppress the rate of acyclic metathesis: reaction between the active metal-carbene chain end and an acyclic olefin in the reaction medium. In particular, we investigate interchain metathesis, which generates linear polymers with "scrambled" chain lengths, and we demonstrate the formation of ring polymers by intrachain backbiting and quantify their content in the reaction product. By controlling the relative rates of propagation versus these side reactions, we prepare ROMP polycyclopentene with low dispersity to substantially higher molecular weights than have been reported previously. Polymerization kinetics are quantitatively described by a kinetic model, which accounts for the reversible binding of added trimethylphosphine to the active chain end.