Modern optical satellites can acquire bundles of panchSromatic (PAN) and multispectral (MS) images of the scene simultaneously. Because of the complexity of the sensors and amount of data involved, an MS image always has lower spatial resolution than the corresponding PAN image. Pansharpening aims at fusing MS images and PAN images, characterized by the spectral content of the former and the spatial details of the latter. There are two main large families of pansharpening algorithms, i.e., component substitution (CS) and multiresolution analysis (MRA). Generally speaking, the CS algorithms have better performance on spatial detail injection, while the MRA shows better spectral content preservation. In this paper, we propose a novel pansharpening algorithm, which combines the conceptions of CS and MRA. This proposed algorithm can be regarded as a generalized version of the existing band-dependent spatial-detail (BDSD) algorithm. A semisimulated dataset and three real datasets are adopted to compare the performance among the generalized-BDSD algorithm and six existing popular pansharpening algorithms. It shows that the proposed method has much lower spectral distortion and good visual appearance. In other words, the proposed method aggregates the advantages of CS and MRA, which shows effectiveness in practice.