Some combinatorial generation problems can be broken into subproblems for which loopless algorithms already exist. We discuss means by which loopless algorithms can be fused to produce a new loopless algorithm that solves the original problem. We demonstrate this method with two new loopless algorithms, MIXPAR and MULTPERM. MIXPAR generates well-formed parenthesis strings containing two different types of parentheses. MULTPERM generates multiset permutations in linear space using only arrays; it is simpler and more efficient than the recent algorithm of Korsh and LaFollette (2004).