  Given a multilevel system coupled to a bath, we use a Feshbach P,Q
partitioning technique to derive an exact trace-nonpreserving master equation
for a subspace $\mathcal{S}_{i}$ of the system. The resultant equation properly
treats the leakage effect from $\mathcal{S}_{i}$ into the remainder of the
system space. Focusing on a second-order approximation, we show that a
one-dimensional master equation is sufficient to study problems of quantum
state storage and is a good approximation, or exact, for several analytical
models. It allows a natural definition of a leakage function and its control,
and provides a general approach to study and control decoherence and leakage.
Numerical calculations on an harmonic oscillator coupled to a room temperature
harmonic bath show that the leakage can be suppressed by the pulse control
technique without requiring ideal pulses.
