The spectral properties of financial correlation matrices can show features known from completely random matrices. A major reason is noise originating from the finite lengths of the financial time series used to compute the correlation matrix elements. In recent years, various methods have been proposed to reduce this noise, i.e. to clean the correlation matrices. This is of direct practical relevance for risk management in portfolio optimization. In this contribution, we discuss in detail the power mapping, a new shrinkage method. We show that the relevant parameter is, to a certain extent, self-determined. Due to the ``chirality'' and the normalization of the correlation matrix, the optimal shrinkage parameter is fixed. We apply the power mapping and the well-known filtering  method to market data and compare them by optimizing stock portfolios. We address the rôle of constraints by excluding short selling in the optimization.

PACS numbers: 89.65.Gh, 05.45.Tp