Bond-length mismatch between alternate layers of the T' ${\mathit{R}}_{2}$${\mathrm{CuO}}_{4}$ intergrowth structure introduces a stretching of the Cu-O bond length in the ${\mathrm{CuO}}_{2}$ planes. The bond-length mismatch is relieved by self-doping. The character of the self-doping is probed by measurements of thermopower and lattice parameters for quenched and air-annealed samples. For R=Sm, Eu, or Gd, oxygen vacancies in the R/${\mathrm{O}}_{2}$/R layers reduce the intralayer compressive stress and introduce antibonding ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$(${\mathit{x}}^{2\mathrm{\ensuremath{-}}}$${\mathit{y}}^{2}$) electrons into the ${\mathrm{CuO}}_{2}$ planes to relieve their intraplanar tensile stress. In ${\mathrm{Nd}}_{2}$${\mathrm{CuO}}_{4}$, a displacement of some oxygen to c-axis sites in the NdO layer permits essentially complete relief of the bond-length mismatch, and the annealed compound is slightly oxidized. The self-doping in ${\mathrm{Pr}}_{2}$${\mathrm{CuO}}_{4}$ involves an internal redox reaction, and the possibilities of Pr(4+/3+) versus peroxide formation are evaluated. The data also indicate a decrease in Madelung energy with increasing Cu-O bond length at the threshold for a transition in n-type transport from small-polaron to intermediate-size-polaron character.