  We study a decoherence reduction scheme that involves an intermediate
measurement on the qubit in an equal superposition basis, in the general
framework of all qubit-environment interactions that lead to qubit pure
decoherence. We show under what circumstances the scheme always leads to a gain
of coherence on average, regardless of the time at which the measurement is
performed, demonstrating its wide range of applicability. Furthermore, we find
that observing an average loss of coherence is a highly quantum effect,
resulting from non-commutation of different terms in the Hamiltonian. We show
the diversity of behavior of coherence as effected by the application of the
scheme, which is skewed towards gain rather than loss, on a variant of the
spin-boson model that does not fulfill the commutation condition.
