RCoO3 perovskites (R = Pr, Tb, Dy, Ho, Er, Tm, Yb, Lu) have been prepared in a polycrystalline form by thermal treatment in air (R = Pr, Tb, Dy), under O2 pressure (200 bar) (R = Ho, Er) or moderate hydrostatic pressures (20 kbar) (R = Tm, Yb, Lu). The samples have been studied at room temperature by high-resolution neutron powder diffraction to follow the evolution of the crystal structures along the series. In all cases, the structure is orthorhombic, space group Pbnm. The spontaneous orthorhombic strain and the tilting angle of the CO6 octahedra progressively increase from Pr to Lu due to simple steric factors. The CoO6 octahedra also undergo a progressive axial deformation along the series, which cannot be ascribed to electronic factors, given the low-spin configuration exhibited at room temperature by Co3+ (t62ge0g) cations for R = Tb…Lu. The stability of the crystal structure is discussed in the light of bond-valence arguments.