We report on recent progress achieved in X-ray laser research at the Institute of Applied Physics of the University of Bern. Using the existing 10-TW Nd: glass CPA (chirped-pulse amplification) laser system in the grazing-incidence pumping (GRIP) scheme, saturated or near-saturated soft-X-ray lasing has been obtained on the 4d. 4p, J = 0-1 lines of barium (Ba, Z = 56), lanthanum (La, Z = 57), and samarium (Sm, Z = 62) at wavelengths down to 7.36 nm, with weak lasing observed at 6.85 nm in Sm. This was achieved with main pulse energies of similar to 10 J at a pulse duration of 1.5 ps. A small-signal gain coefficient of similar to 30 cm-1 and a gain-length product of similar to 16 at saturation have been measured in the case of the 9.2-nm Ba laser. Crucial to these results was the introduction of a second, relatively intense (similar to 20%) prepulse less than 50 ps before the main pulse, in addition to the 2.8% prepulse that irradiated the target similar to 3 ns earlier. Travelling-wave excitation was used throughout.