Biobanks often contain several phenotypes relevant to a given disorder, and researchers face complex tradeoffs between shallow phenotypes (high sample size, low specificity and sensitivity) and deep phenotypes (low sample size, high specificity and sensitivity). Here, we study an extreme case: Major Depressive Disorder (MDD) in UK Biobank. Previous studies found that shallow and deep MDD phenotypes have qualitatively distinct genetic architectures, but it remains unclear which are optimal for scientific study or clinical prediction. We propose a new framework to get the best of both worlds by integrating together information across hundreds of MDD-relevant phenotypes. First, we use phenotype imputation to increase sample size for the deepest available MDD phenotype, which dramatically improves GWAS power (increases #loci ~10 fold) and PRS accuracy (increases R2 ~2 fold). Further, we show the genetic architecture of the imputed phenotype remains specific to MDD using genetic correlation, PRS prediction in external clinical cohorts, and a novel PRS-based pleiotropy metric. We also develop a complementary approach to improve specificity of GWAS on shallow MDD phenotypes by adjusting for phenome-wide PCs. Finally, we study phenotype integration at the level of GWAS summary statistics, which can increase GWAS and PRS power but introduces non-MDD-specific signals. Our work provides a simple and scalable recipe to improve genetic studies in large biobanks by combining the sample size of shallow phenotypes with the sensitivity and specificity of deep phenotypes.