New functions requiring multiple mutations are thought to be evolutionarily feasible if they can be achieved by means of adaptive paths-successions of simple adaptations each involving a single mutation.  The presence or absence of these adaptive paths to new function therefore constrains what can evolve.  But since emerging functions may require costly over-expression to improve fitness, it is also possible for reductive (i.e., cost-cutting) mutations that eliminate over-expression to be adaptive.  Consequently, the relative abundance of these kinds of adaptive paths--constructive paths leading to new function versus reductive paths that increase metabolic efficiency--is an important evolutionary constraint.  To study the impact of this constraint, we observed the paths actually taken during long-term laboratory evolution of an Escherichia coli strain carrying a doubly mutated trpA gene. The presence of these two mutations prevents tryptophan biosynthesis.  One of the mutations is partially inactivating, while the other is fully inactivating, thus permitting a two-step adaptive path to full tryptophan biosynthesis. Despite the theoretical existence of this short adaptive path to high fitness, multiple independent lines grown in tryptophan-limiting liquid culture failed to take it.  Instead, cells consistently acquired mutations that reduced expression of the double-mutant trpA gene.  Our results show that competition between reductive and constructive paths may significantly decrease the likelihood that a particular constructive path will be taken. This finding has particular significance for models of gene recruitment, since weak new functions are likely to require costly over-expression in order to improve fitness. If reductive, cost-cutting mutations are more abundant than mutations that convert or improve function, recruitment may be unlikely even in cases where a short adaptive path to a new function exists.