Complex traits can require the accumulation of multiple mutations that are individually deleterious. Their evolution requires a fitness valley to be crossed, which can take relatively long time spans. A new evolutionary mechanism is described that accelerates the emergence of complex phenotypes, based on a "division of labor" game and the occurrence of cheaters. If each intermediate mutation leads to a product that can be shared with others, the complex type can arise relatively quickly as an emergent property among cooperating individuals, without any given individual having to accumulate all mutations. Moreover, the emergence of cheaters that destroy cooperative interactions can lead to the emergence of individuals that have accumulated all necessary mutations on a time scale that is significantly faster than observed in the absence of cooperation and cheating. Application of this mechanism to somatic and microbial evolution is discussed, including evolutionary processes in tumors, biofilms, and viral infections.