We derive conditions for the unique and simultaneous recovery of chromophore concentrations and scattering coefficients in multispectral continuous-wave diffuse optical tomography. These conditions depend strongly on measurement wavelengths. We introduce and demonstrate a general methodology for choosing those wavelengths, which yields superior separation of scattering from absorption and superior separation of one chromophore from another. Application of these concepts should significantly improve the fidelity of continuous-wave diffuse near-infrared optical tomography in tissues.