We develop new heuristics and an exact algorithm for calculating the amount of hybridization between two rooted binary phylogenetic trees. Calculating the minimum number of hybridization events is NP-hard, but essential to understanding the modeling of reticulation processes such as hybridization, horizontal gene transfer, and recombination. We give new lower bounds for the hybridization number that are very useful in limiting search times for exact answers and in conjunction with existing upper bounds to "sandwich" the true answer. We analyze the algorithms experimentally on both biological and simulated data.