Ideal three-dimensional concentration has been sought for decades in the solar and optical worlds. Nonimaging optics has been able to achieve this thermodynamic maximum concentration limit with certain symmetrical designs, but three-dimensional concentration in which acceptance angles are not symmetric has been a challenge for researchers. Our study outlines a new design approach that hopes to move toward the development of an ideal 3D asymmetric concentrator based on the current asymmetric compound parabolic concentrator (ACPC) design principles. A geometric scheme to revolve a variable ACPC curve about a central axis is presented. The 3D ACPC is compared with a standard compound parabolic concentrator (CPC) in a tilted and angular truncated case. Each design was characterized for performance by examining the angular acceptance/illumination region in angular direction cosine space. Ideal performance was demonstrated for the 3D ACPC design for an off axis circular Lambertian acceptance region in direction cosine plots, whereas the CPC designs failed to maintain a circular Lambertian distribution. High-aperture tilt angles demonstrated an interesting “flaring” of the aperture, which caused a decline in ideal performance. Despite design deformations at high-aperture angles, the 3D ACPC design method presented here is a step toward ideal 3D asymmetric concentration.