White　light-emitting　diode　(LED)　spectra　for　general　lighting　should　be　designed　for　high　luminous　efficacy　as　well　as　good　color　rendering,　which　are　generally　in　a　trade-off　relationship.　White　LEDs　have　uncountable　metameres,　they　have　different　luminous　efficacy　and　color　rendering.　Appropriate　designed　trichromatic　and　tetrachromatic　LED-based　white　LEDs　are　presented　that　have　acceptable　color　rendering　as　well　as　good　luminous　efficacy.　Triachromatic　white　LEDs,　with　a　wavelength　combination　of　460,　540,　and　615　nm,　offer　high　general　color　rendering　index　exceeding　89,　and　luminous　efficacy　3361m/W.　The　general　color　rendering　index　of　tetrachromatic　LED-based　white　LEDs　combined　from　460,　525,　590,　and　640　nm　is　95,　the　luminous　efficacy　is　3061m/W.　Further　analysis　shows　the　changing　trends　of　the　luminous　efficacy,　color　rendering　and　the　chromaticity　coordinate　of　the　optimized　trichromatic　and　tetrachromatic　white　LEDs　depending　on　the　wavelength　shift　of　the　primary　LEDs.　For　the　optimized　trichromatic　white　LEDs,　both　the　luminous　efficacy　and　color　rendering　change　more　with　the　wavelength　shifts　of　the　primary　red　LEDs　than　with　the　wavelength　shifts　of　the　blue　and　green　LEDs.　For　the　optimized　tetrachromatic　white　LEDs,　the　changes　of　the　luminous　efficacy　caused　by　the　wavelength　shifts　of　one　red　LED　are　smaller　than　the　changes　of　trichromatic　white　LEDs.　And　the　wavelength　shifts　of　the　red　primary　LED　that　have　shorter　wavelength　affect　the　color　rendering　more　than　the　other　primary　LEDs.　The　wavelength　shifts　of　the　blue　primary　LED　change　the　chromaticity　coordinate　of　the　white　LEDs　more.　The　small　changes　of　the　chromaticity　coordinate　of　the　white　LED　do　not　mean　small　changes　of　the　k　and　R-a.　(c)　2006　Elsevier　Ltd.　All　rights　reserved.