A white LED assembly includes a blue LED die attached to a substrate. A first volume of a first luminescent material surrounds the blue LED die in a lateral dimension such that none of the first luminescent material is disposed directly over the blue LED die. The first luminescent material includes a relatively inefficient phosphor having a peak emission wavelength longer than 620 nm and includes substantially no phosphor having a peak emission wavelength shorter than 620 nm. A second volume of a second luminescent material is disposed over the first volume and the blue LED die. The second luminescent material includes a relatively efficient phosphor having a peak emission wavelength shorter than 620 nm and includes substantially no phosphor having a peak emission wavelength longer than 620 nm. Placement of the first and second luminescent materials in this way promotes removal of heat from the inefficient phosphor and reduces the likelihood of interabsorption.