With a viev to the goal of net energy production from a DT microexplosion, we study two ideas (methods) through which (separately or in combination) energy may be "concentrated" into a small volume and short period of time-the so-called space-time energy densification or compression. We first discuss the advantages and disadvantages of lasers and relativistic electron-beam {E-beam) machines as the sources of such energy and identify the amplification of laser pulses as a key factor in energy compression. The pulse length of present relativistic E-beam machines is the most serious linitatioo of this pulsed-power source. The first energy-compression idea we discuss is the reasonably efficient production of short-duration, hi^h-current relativistic electron pulses by the self interruption and restrii;e of a current in a plasna pinch due to the rapid onset uf strong turbulence. A 1-MJ plasma focus based on this method is nearing completion at this Laboratory. The second energy-compression Idea is based on laserpulse producti , through the parametric amplification of a self-similar or solitary wave pulse, for which analogs can be found in other wave processes. Specifically, the second energy-compression idea is a proposal for parametric amplification of a solitary, transverse magnetic pulse in a coaxial cavity with a Bennett dielectric rod as an inner coax. Amplifiers of this type can be driven by the pulsed power frorr a relativistic K-beam machine. If the end of the inner dielectric coax is nade of LiDT or another fusionable material, the amplified pulse can directly drive a fusion reaction-there would be no need to switch the pulse out of the system toward a remote target.