  Pseudoscalar-meson photoproduction is characterized by four complex reaction
amplitudes. A complete set is a minimum theoretical set of observables that
allow to determine these amplitudes unambiguously. It is studied whether
complete sets remain complete when experimental uncertainty is involved. To
this end, data from the GRAAL Collaboration and simulated data from a realistic
model, both for the $\gamma p \to K^+ \Lambda$ reaction, are analyzed in the
transversity representation of the reaction amplitudes. It is found that only
the moduli of the transversity amplitudes can be determined without ambiguity
but not the relative phases.
