A solution to develop high-brightness incoherent sources consists in luminescent concentration. Indeed, the absorption/emission process in a high index medium allows us to circumvent the brightness conservation law by the confinement of the light in 1 or 2 dimensions. In practice, Ce-doped luminescent concentrators pumped with InGaN LED exceed LED's brightness by one order of magnitude. This work shows how light confinement in 3 dimensions increases the brightness by an additional order of magnitude. Thanks to an analytical approach validated by experimental results, this concept gives new degrees of freedom for the design of luminescent concentrators and paves the way to a generation of incoherent sources among the brightest ever designed.