We report a new strategy based on mercury cation exchange in nonpolar solvents to prepare bright and compact alloyed quantum dots (QDs) (HgxCd1-xE, where E = Te, Se, or S) with equalized particle size and broadly tunable absorption and fluorescence emission in the near-infrared. The main rationale is that cubic CdE and HgE have nearly identical lattice constants but very different band gap energies and electron/hole masses. Thus, replacement of Cd2+ by Hg2+ in CdTe nanocrystals does not change the particle size, but it greatly alters the band gap energy. After capping with a multilayer shell and solubilization with a multidentate ligand, this class of cation-exchanged QDs are compact (6.5 nm nanocrystal size and 10 nm hydrodynamic diameter) and very bright (60-80% quantum yield), with narrow and symmetric fluorescence spectra tunable across the wavelength range from 700 to 1150 nm.