  This paper reconsiders the claimed rapidity of a scheme for the purification
of the quantum state of a qubit, proposed recently in Jacobs 2003 Phys. Rev.
A67 030301(R). The qubit starts in a completely mixed state, and information is
obtained by a continuous measurement. Jacobs' rapid purification protocol uses
Hamiltonian feedback control to maximise the average purity of the qubit for a
given time, with a factor of two increase in the purification rate over the
no-feedback protocol. However, by re-examining the latter approach, we show
that it mininises the average time taken for a qubit to reach a given purity.
In fact, the average time taken for the no-feedback protocol beats that for
Jacobs' protocol by a factor of two. We discuss how this is compatible with
Jacobs' result, and the usefulness of the different approaches.
