The univariate direct quadrature spanning tree (DQST) method was evaluated with respect to accuracy and computational cost. This included a convergence analysis over the discretization of the breakage term and an accuracy analysis of the smoothing procedure. We also proposed many enhancements to the method, including a second-order time integration scheme, a new initialization method and its extension for cases involving growth. We have shown that the original smoothing procedure does not conserve the second-order moment of the distribution. In order to guarantee its conservation, a new smoothing method was proposed. The usage of the new smoothing method combined with the second-order time integration scheme reduced the moment errors by several orders of magnitude with a modest increase in the computational cost. (C) 2017 Elsevier B.V. All rights reserved.