The orthogonal subspace projection (OSP) algorithm, which is used to process mixed pixels in hyperspectral images, is discussed frequently in the remote sensing literature. A recent paper discussed ways to derive the OSP and the use of OSP as a target detector or for material abundance estimation. However, a technique called the constrained signal detector (CSD) outperforms the OSP technique. OSP is equivalent to the unconstrained least-squares estimate of the abundance of a particular material in a mixed pixel. CSD is equivalent to the constrained least-squares abundance estimate. It is shown through theory and simulation that the constrained method (CSD) outperforms the unconstrained technique (OSP) for the problems of target detection and material abundance estimation in mixed pixels.