Economic theory suggests that selective immigration policies based on observable characteristics will affect unobservable migrant quality. Little empirical evidence exists on this hypothesis. We quantify traditionally unobservable components of migrant quality in Australia, a high-migrant share OECD country with a selective immigration policy. We proxy migrant quality with widely-accepted measures of personality and cognitive ability. Both first- and second-generation immigrants outperform natives on socially-beneficial personality traits. While first-generation migrants suffer language-ability penalties, their off-spring overcome these penalties and outperform natives in cognitive ability. Immigrants do not outperform natives in the labor market, a finding which may be explained by heterogeneous wage returns to non-cognitive ability.