Although the neutral theory of molecular evolution was proposed to explain DNA and protein sequence evolution, in principle it could also explain phenotypic evolution. Nevertheless, overall, phenotypes should be less likely than genotypes to evolve neutrally. I propose that, when phenotypic traits are stratified according to a hierarchy of biological organization, the fraction of evolutionary changes in phenotype that are adaptive rises with the phenotypic level considered. Consistently, molecular traits are frequently found to evolve neutrally whereas a large, random set of organismal traits were recently reported to vary largely adaptively. Many more studies of unbiased samples of phenotypic traits are needed to test the general validity of this hypothesis.