  A normalized positive operator measure $X\mapsto E(X)$ has the
norm-1-property if $\no{E(X)}=1$ whenever $E(X)\ne O$. This property reflects
the fact that the measurement outcome probabilities for the values of such
observables can be made arbitrary close to one with suitable state
preparations. Some general implications of the norm-1-property are
investigated. As case studies, localization observables, phase observables, and
phase space observables are considered.
