The compact conventional six-period torsatron L-V with an aspect ratio of A = 3 has been considered as a starting point for further computational optimization of the collisionless confinement of the guiding center orbits of fusion a particles. The configurations obtained possess improved neoclassical transport together with an equilibrium beta limit at a level of approximate to 10%. The optimization of magnetohydrodynamic (MHD) stability and the coil design are underway. (C) 2003 MAIK "Nauka/Interperiodica".