Nuclear deformation effects on the binding energies in heavy ions are investigated. Approximate formulas for the nuclear-size correction and the isotope shift for deformed nuclei are derived. Combined with direct numerical evaluations, these formulas are employed to reanalyze experimental data on the nuclear-charge-distribution parameters in U 238 and to revise the nuclear-size corrections to the binding energies in H- and Li-like U 238. As a result, the theoretical uncertainties for the ground-state Lamb shift in U 238 91+ and for the 2 p1/2 -2s transition energy in U 238 89+ are significantly reduced. The isotope shift of the 2 pj -2s transition energies for N 142 d57+ and N 150 d57+ is also evaluated including nuclear size and nuclear recoil effects within a full QED treatment.