Step 1: Rank the Mapleson systems by how much fresh gas flow (FGF) is needed to avoid rebreathing during spontaneous breathing; the lower the FGF requirement, the more efficient the circuit.
Step 2: In the Mapleson A or Magill arrangement, the expiratory valve sits close to the patient. On expiration, alveolar gas is vented first, while fresh gas refills the reservoir bag, so the next breath draws minimal carbon dioxide.
Step 3: This geometry lets $FGF \approx$ alveolar minute ventilation prevent rebreathing, which is the most economical of all the systems for a spontaneously breathing patient.
Step 4: The same circuit becomes inefficient for controlled ventilation (where Mapleson D excels), but for the spontaneous mode asked here the answer is Mapleson A.\[\boxed{\text{Mapleson A}}\]