Summary: We provide a general framework for finding portfolios that perform well out-of-sample in the presence of estimation error. This framework relies on solving the traditional minimum-variance problem but subject to the additional constraint that the norm of the portfolio-weight vector be smaller than a given threshold. We show that our framework nests as special cases the shrinkage approaches of R. Jagannathan and T. Ma “[Risk reduction in large portfolios: why imposing the wrong constraints helps”, J. Finance 58, 1651–1684 (2003)] and O. Ledoit and M. Wolf [J. Multivariate Anal. 88, No. 2, 365–411 (2004; Zbl 1032.62050)] and the \(1/N\) portfolio studied in by DeMiguel et al. We also use our framework to propose several new portfolio strategies. For the proposed portfolios, we provide a moment-shrinkage interpretation and a Bayesian interpretation where the investor has a prior belief on portfolio weights rather than on moments of asset returns. Finally, we compare empirically the out-of-sample performance of the new portfolios we propose to 10 strategies in the literature across five data sets. We find that the norm-constrained portfolios often have a higher Sharpe ratio than the portfolio strategies in Jagannathan and Ma, Ledoit and Wolf, the \(1/N\) portfolio, and other strategies in the literature, such as factor portfolios.