They recruited 12 healthy young men who normally slept well and kept them awake for 38 hours during which they had tests to measure brain function and memory, as well as physical strength.
The recruits did the experiment after getting their normal amount of sleep, then repeated it after going to bed two hours earlier for six nights beforehand.
The results, reported in the American Journal of Sports Medicine, showed physical and mental performance was better when they "banked" sleep in advance.
But British sleep experts said the study was small and there is no scientific rationale behind the theory that stockpiling sleep actually works.
Professor Jim Horne, former head of the Sleep Research Centre at Loughborough University, said: "You cannot bank sleep in advance. The best way to recover from a late night is to have a daytime nap of no more than 20 minutes."
Independent sleep expert Dr Neil Stanley said the findings were too weak to claim accumulating sleep had any real benefit.