  A fundamental limit to the stability of a single-ion optical frequency
standard is set by quantum noise in the measurement of the internal state of
the ion. We discuss how the interrogation sequence and the processing of the
atomic resonance signal can be optimized in order to obtain the highest
possible stability under realistic experimental conditions. A servo algorithm
is presented that stabilizes a laser frequency to the single-ion signal and
that eliminates errors due to laser frequency drift. Numerical simulations of
the servo characteristics are compared to experimental data from a frequency
comparison of two single-ion standards based on a transition at 688 THz in
171Yb+. Experimentally, an instability sigma_y(100 s)=9*10^{-16} is obtained in
the frequency difference between both standards.
