Perhaps the most universally accepted precept of prudent investing is diversify, yet this precept grossly oversimplifies the challenge of portfolio construction. Consider a typical investor who relies on domestic equities to drive portfolio construction. Consider a typical investor who relies on domestic equities to drive portfolio growth. This investor will seek to diversify this exposure by including assets that have low correlations with domestic equities. Yet the correlations, as typically measured over the full sample of returns, often belie an asset’s diversification properties in market environments when diversification is most needed, for example, when domestic equities perform poorly. Moreover, upside diversification is undesirable; investors should seek unification on the upside. Ideally, the assets chosen to complement a portfolio’s main engine of growth should diversify this asset when it performs poorly and move in tandem with it when it performs well. In this article, we will first describe the mathematics of conditional correlations assuming returns are normally distributed. Then, we will present empirical results across a wide variety of assets, which reveal that, unlike the theoretical profiles, empirical correlations are significantly asymmetric. We are not the first to uncover correlation asymmetries, but our empirical investigation updates prior research and extends the analysis to a much broader set of assets. Finally, we will show that a portfolio construction technique called full-scale optimization produces portfolios in which the component assets exhibit relatively lower correlations on the downside and higher correlations on the upside than mean-variance optimization.