Predicting next items of sequences of symbols has many applications in a wide range of domains. Several sequence prediction models have been proposed such as DG, All-k-order Markov and PPM. Recently, a model named Compact Prediction Tree (CPT) has been proposed. It relies on a tree structure and a more complex prediction algorithm to offer considerably more accurate predictions than many state-of-the-art prediction models. However, an important limitation of CPT is its high time and space complexity. In this article, we address this issue by proposing three novel strategies to reduce CPT’s size and prediction time, and increase its accuracy. Experimental results on seven real life datasets show that the resulting model (CPT+) is up to 98 times more compact and 4.5 times faster than CPT, and has the best overall accuracy when compared to six state-of-the-art models from the literature: All-K-order Markov, CPT, DG, Lz78, PPM and TDAG.