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 reanalyse experimental data on the nuclear-charge-distribution parameters in $^{238}textrm{U}$ and to revise the nuclear-size corrections to the binding energies in H- and Li-like $^{238}textrm{U}$. As a result, the theoretical uncertainties for the ground-state Lamb shift in $^{238}textrm{U}^{91+}$ and for the $2p_{1/2}-2s$ transition energy in $^{238}textrm{U}^{89+}$ are significantly reduced. The isotope shift of the $2p_{j}-2s$ transition energies for $^{142}textrm{Nd}^{57+}$ and $^{150}textrm{Nd}^{57+}$ is also evaluated including nuclear size and nuclear recoil effects within a full QED treatment.
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