  Purification of mixed states in Quantum Mechanics, by which we mean the
transformation into pure states, has been viewed as an {\it Operation} in the
sense of Kraus et al and explicit {\it Kraus Operators} \cite{kra1,kra2,kra3}
have been constructed for two seperate purification protocols. The first one,
initially due to Schrodinger \cite{sch} and subsequently elaborated by
Sudarshan et al \cite{sudar}, is based on the {\it preservation of
probabilities}. We have constructed a second protocol here based on {\it
optimization of fidelities}. Both purification protocols have been implemented
on a single qubit in an attempt to improve the fidelity of the purified post
measurement state of the qubit with the initial pure state. We have considered
both {\it complete} and {\it partial} measurements and have established bounds
and inequalities for various fidelities. We show that our purification protocol
leads to better state reconstruction, most explicitly so, when partial
measurements are made.
