Quantum dots with a core/shell/shell structure consisting of an alloyed core of InAs(x)P(1-x), an intermediate shell of InP, and an outer shell of ZnSe were developed. The InAs(x)P(1-x) alloyed core has a graded internal composition with increasing arsenic content from the center to the edge of the dots. This compositional gradient results from two apparent effects: (1) the faster reaction kinetics of the phosphorus precursor compared to the arsenic precursor, and (2) a post-growth arsenic-phosphorus exchange reaction that increases the arsenic content. The cores have a zinc blend structure for all compositions and show tunable emission in the near-infrared (NIR) region. A first shell of InP leads to a red-shift and an increase in quantum yield. The final shell of ZnSe serves to stabilize the dots for applications in aqueous environments, including NIR biomedical fluorescence imaging. These NIR-emitting core/shell/shell InAs(x)P(1-x)/InP/ZnSe were successfully used in a sentinel lymph node mapping experiment.