The complexity of merging two sorted sequences into one is linear in the worst case as well as in the average case. There are, however, instances for which a sublinear number of comparisons is sufficient. We consider the problem of measuring and exploiting such instance easiness. The merging algorithm presented, Adaptmerge, is shown to optimally adapt to different kinds of measures of instance ... [Show full abstract] easiness. In the sorting problem, the concept of instance easiness has received a lot of attention and is interpreted by a measure of presortedness. We apply Adaptmerge in the already adaptive sorting algorithm Natural Merge Sort. The resulting algorithm optimally adapts to several, known and new, measures of presortedness. We also prove some interesting results concerning the relation between measures of presortedness proposed in the literature.