We propose a scheme for a compact nickel-like-tungsten soft-x-ray lase
r operating on the 4d-4p, J=0-1 transition at 43.2 Angstrom. High gain
s are achieved by operating at high electron densities (n(e)>10(22) cm
(-3)). In this regime, the gain during nonequilibrium ionization can g
reatly exceed that of the steady state. The duration of this transient
gain is on the order of the ionization time, which makes picosecond-p
ulsed optical pumps ideal. Two target designs, solid tungsten slabs, a
nd tungsten aerogels foams, are considered. We predict gains of 220 cm
(-1) for a 1-mu m pump of intensity I=2.5X10(16) W/cm(2). [S1050-2947(
98)06602-5].