  In this paper we address the problem of optimal reconstruction of a quantum
state from the result of a single measurement when the original quantum state
is known to be a member of some specified set. A suitable figure of merit for
this process is the fidelity, which is the probability that the state we
construct on the basis of the measurement result is found by a subsequent test
to match the original state. We consider the maximisation of the fidelity for a
set of three mirror symmetric qubit states. In contrast to previous examples,
we find that the strategy which minimises the probability of erroneously
identifying the state does not generally maximise the fidelity.
