LED packages, and LED lamps and bulbs, are disclosed that are arranged to minimize the CRI and efficiency losses resulting from the overlap of conversion material emission and excitation spectrum. In different devices having conversion materials with this overlap, the present invention arranges the conversion materials to reduce the likelihood that re-emitted light from a first conversion materials will encounter the second conversion material to minimize the risk of re-absorption. In some embodiments this risk is minimized by different arrangements where there is separation between the two phosphors. In some embodiments this separation results less than 50% of re-emitted light from the one phosphor passing into the phosphor where it risks re-absorption.