Nuclear moments of odd-A neon isotopes in the range 17 <= A <= 25 have been determined from optical hyperfine structures measured by collinear fast-beam laser spectroscopy. The magnetic dipole moments of Ne-17, Ne-23, and Ne-25, as well as the electric quadrupole moment of Ne-23, are either reported for the first time or improved considerably. The measurements also decide for a 1/2(+) ground state of Ne-25. The behavior of the magnetic moments of the proton drip-line nucleus Ne-17 and its mirror partner N-17 suggests isospin symmetry. Thus, no clear indication of an anomalous nuclear structure is found for Ne-17. The magnetic moments of the investigated nuclei are discussed in a shell-model approach.