Tint and Brightness Question

It's my understanding that coloured LEDs will appear brighter than white ones, in part due to the fact that our perceptual system recognizes some wavelengths better than others. I am wondering, if this is the case, could the tinting of a white LED significantly affect the percieved brightness of the beam? If this is true, and I'm going to get an LED that is not super white, what colour should I get so I can at least improve the brightness of my beam?

Here is a discussion of the effects of color temperature on perceived brightness. Basically, a light source that is bluer is perceived as brighter than one that is yellower, at least at lighting levels typical of indoors or lower. Therefore, all other things being equal, a blue-white LED will appear brighter than a pure white one which in turn will be brigher than a yellow-white one. Complicating matters, and not mentioned in that link, is the fact that light sources with greater color rendering (higher CRI) also appear brighter. For example, a 3500K, 86 CRI fluorescent tube will seem brighter than a 3500K, 78 CRI tube. However, in comparing LEDs of the same type (lets say LIIIs), CRI is generally similar across tint variations so the tint is all that matters. Also, past a point blue tinted white lights don't appear brighter. I think this occurs around roughly 6500K to 7000K.