Vine copulas are pair-copula constructions enabling multivariate dependence modeling in terms of bivariate building blocks. One of the main tasks of fitting a vine copula is the selection of a suitable tree structure. For this the prevalent method is a heuristic called Di{ss}manns algorithm. It sequentially constructs the vines trees by maximizing dependence at each tree level, where dependence is measured in terms of absolute Kendalls $tau$. However, the algorithm disregards any implications of the tree structure on the simplifying assumption that is usually made for vine copulas to keep inference tractable. We develop two new algorithms that select tree structures focused on producing simplified vine copulas for which the simplifying assumption is violated as little as possible. For this we make use of a recently developed statistical test of the simplifying assumption. In a simulation study we show that our proposed methods outperform the benchmark given by Di{ss}manns algorithm by a great margin. Several real data applications emphasize their practical relevance.
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