The optimal spectral parameters and photometric performances of white LEDs with red LEDs instead of phosphor (pc/R-WLEDs) for the color fidelity index (Rf) above 97 at correlated color temperatures (CCTs) of 2700 K to 6500 K have been obtained based on the luminous efficacy (LE) model. We have first reported four real pc/R-WLEDs with Rfs of 96–97 and LEs of 120–124 lm/W at CCTs of 2969 K, 4468 K, 5682 K, and 6558 K by using blue (448 nm) and red (650 nm) LEDs, as well as green (507 nm) and yellow (586 nm) phosphors. As compared with phosphor-converted white LEDs (pc-WLEDs) as well as quantum dots white LEDs (QD-WLED), it was found that the pc/R-WLEDs, not the QD-WLED as widely expected, make strong candidates for excellent color rendition, especially in the low color temperature range, for replacing current pc-WLEDs in the future.