We recently proposed the Edgewise Greedy Algorithm (EGA) for learning a decomposable Markov network of treewidth k approximating a given joint probability distribution of n discrete random variables. The main ingredient of our algorithm is the stepwise forward selection algorithm (FSA) due to Deshpande, Garofalakis, and Jordan. EGA is an efficient alternative to the algorithm (HGA) by Malvestuto, which constructs a model of treewidth k by selecting hyperedges of order k+1. In this paper, we present results of empirical studies that compare HGA, EGA and FSA-K which is a straightforward application of FSA, in terms of approximation accuracy (measured by KL-divergence) and computational time. Our experiments show that (1) on the average, all three algorithms produce similar approximation accuracy; (2) EGA produces comparable or better approximation accuracy and is the most efficient among the three. (3) Malvestuto's algorithm is the least efficient one, although it tends to produce better accuracy when the treewidth is bigger than half of the number of random variabls; (4) EGA coupled with local search has the best approximation accuracy overall, at a cost of increased computation time by 50 percent.