  We use soft heaps to obtain simpler optimal algorithms for selecting the
$k$-th smallest item, and the set of~$k$ smallest items, from a heap-ordered
tree, from a collection of sorted lists, and from $X+Y$, where $X$ and $Y$ are
two unsorted sets. Our results match, and in some ways extend and improve,
classical results of Frederickson (1993) and Frederickson and Johnson (1982).
In particular, for selecting the $k$-th smallest item, or the set of~$k$
smallest items, from a collection of~$m$ sorted lists we obtain a new optimal
"output-sensitive" algorithm that performs only $O(m+\sum_{i=1}^m \log(k_i+1))$
comparisons, where $k_i$ is the number of items of the $i$-th list that belong
to the overall set of~$k$ smallest items.
