  We analyze quantum state-transfer optimization within hybrid open systems,
from a "noisy" (write-in) qubit to its "quiet" counterpart (storage qubit).
Intriguing interplay is revealed between our ability to avoid bath-induced
errors that profoundly depend on the bath-memory time and the limitations
imposed by leakage out of the operational subspace. Counterintuitively, under
no circumstances is the fastest transfer optimal (for a given transfer energy).
