  In this paper we consider feedback control algorithms for the rapid
purification of a bipartite state consisting of two qubits, when the observer
has access to only one of the qubits. We show 1) that the algorithm that
maximizes the average purification rate is not the same as that that for a
single qubit, and 2) that it is always possible to construct an algorithm that
generates a deterministic rate of purification for {\em both} qubits. We also
reveal a key difference between projective and continuous measurements with
regard to state-purification.
