  We consider the fundamental problem of internally sorting a sequence of $n$
elements. In its best theoretical setting QuickMergesort, a combination
Quicksort with Mergesort with a Median-of-$\sqrt{n}$ pivot selection, requires
at most $n \log n - 1.3999n + o(n)$ element comparisons on the average. The
questions addressed in this paper is how to make this algorithm practical. As
refined pivot selection usually adds much overhead, we show that the
Median-of-3 pivot selection of QuickMergesort leads to at most $n \log n -
0{.}75n + o(n)$ element comparisons on average, while running fast on
elementary data. The experiments show that QuickMergesort outperforms
state-of-the-art library implementations, including C++'s Introsort and Java's
Dual-Pivot Quicksort. Further trade-offs between a low running time and a low
number of comparisons are studied. Moreover, we describe a practically
efficient version with $n \log n + O(n)$ comparisons in the worst case.
