A part of the two-loop self-energy correction, the so-called P term, is eva
luated numerically for the Is state to all orders in Za. Our calculation. c
ombined with the previous investigation [S. Mallampalli and J. Sapirstein.
Phys. Rev.A57, 1548 (1998)]. yields the total answer for the two-loop self-
energy correction in H-like uranium and bismuth. As a result. the major unc
ertainty is eliminated from the theoretical prediction for the Lamb shift i
n these systems, The total value of the ground-state Lamb shift in H-like u
ranium is found to be 463.95(50) eV.