The goal of the experiments on “Module A-5” and S-300 machines for some 15 years was to study the “liner-converter” inertial confinement fusion (ICF) scheme. A new class of fast instabilities of z pinches was studied both in experiments and in analytical theory. Stabilization of the light liner has been achieved by means of an extrinsic magnetic field. Formation of thin overheated current-carrying shells has been predicted analytically and seems to be really observed. Both theory and simulations predict growing Te and heat flux onto the converter by using heterogeneous z pinches with spatially separated regions of efficient energy exchange and of efficient heat conductivity. In our first experiments of this kind, impurities were inserted by means of placing thin glass fibers into a He jet. Growing intensity of the spectral lines of He-like chlorine from the cathode surface confirms the growth of heat flux. Theoretical investigations and 2.5-D simulations were devoted to some basic points of this program.