Summary: We propose a novel methodology for constructing optimal portfolios in the presence of (i) model parameter uncertainty and (ii) user-specified constraints on the portfolio weights. This is a challenging problem, in large part because the constraint conditions generally preclude the derivation of closed-form solutions even in the absence of parameter uncertainty. Yet, in this article, we succeed in producing a practical solution, which is based on a herein proposed technique that we call a “perturbation method”. The method relies on a specially devised resampling procedure, whose performance is shown in simulations to compare favorably to other methods from the literature on portfolio optimization.