The results of explorations of non-traditional solutions of beam transport which could raise the electron cooling rates and efficiency are presented. The proposed optical elements, methods, and conceptual designs are summarized in the following. (1) Magnetized electron beam acceleration and transport with discontinuous solenoid to provide matching between the electron gun and solenoid of the cooling section. These concepts allow the possibility to design and build economical, high beam quality accelerators for electron cooling over a wide energy range, up to that suited for hadron colliders. (2) A special beam adapter (skew quadrupole block) to transform between a magnetized and a flat beam state. This element meets a variety of uses in electron cooling trends. (3) Injectors with ring-shaped cathodes and resonance concentrators of hollow beams involving (optionally) beam adapters. (4) An isochronous (at no RF) electron recirculator ring with a solenoid in the cooling section and beam adapters. (5) Electron storage rings incorporating strong wigglers, solenoid in cooling section with beam adapters, non-coupled focusing outside the cooling section, and (optionally) a strong longitudinal optics for beam compression in wigglers. (6) Hadron beam optics in the cooling section with non-extended beams and dispersion introduced in order to maximize the transverse cooling rate. (7) Low-energy cooling with matched electron and hadron beams. (8) Low-energy cooling with hollow beams.