  We generalize a well-known algorithm for the generation of all subsets of a
set in lexicographic order with respect to the sets as lists of elements
(subset-lex order). We obtain algorithms for various combinatorial objects such
as the subsets of a multiset, compositions and partitions represented as lists
of parts, and for certain restricted growth strings. The algorithms are often
loopless and require at most one extra variable for the computation of the next
object. The performance of the algorithms is very competitive even when not
loopless. A Gray code corresponding to the subset-lex order and a Gray code for
compositions that was found during this work are described.
