  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.
