full result of Ref. [@pachuckiD] should be 1.665(16) meV. On the other hand, Ref. [@Friar:2013rha] estimates the Lamb shift in the zero-range approximation to be 1.912 meV (1.942 with further corrections), and quotes the result of Ref. [@pachuckiD] in that approximation as 1.899 meV. These numbers are close to each other, nevertheless, we point out that the differences are not small, especially compared to the uncertainty of $16\,\mu$eV claimed in Ref. [@pachuckiD]. As mentioned above, the correct account of the nucleon polarizability corrections alone shifts the result of Ref. [@pachuckiD] by $15\,\mu$eV that exhausts the claimed precision of the calculation. In Ref. [@Ji:2013oba] the calculation of the polarizability correction is reexamined and higher-order relativistic corrections from longitudinal and transverse two-photon exchanges were included, leading to an additional contribution of $18\,\mu$eV.

Electronic Hydrogen
===================

To complete the discussion, we assess the nuclear polarizability correction for the $nS$-levels in the usual (electronic) deuterium, too. In particular, the isotopic shift measurement of $1S-2S$ splitting of Ref. [@Parthey:2010] relies on the theoretical estimate according to Ref. [@FriarPayne], E\_[2S-1S]{}\^[e-D]{}&=&19.04(7)[kHz]{}, where the polarizability correction of 18.58(7) kHz and the elastic contribution of 0.46 kHz were added together. Ref. [@milshtein] gives a somewhat different result, E\_[2S-1S]{}\^[e-D]{}&=&19.25[kHz]{}, with 