We have studied the sublimation of ice buried beneath ≤200 mm of JSC Mars-1 model regolith under simulated Mars conditions. As expected, even thin layers of regolith cause large decreases in sublimation rate, up to one order of magnitude at 50 mm. When the depth of the regolith was 50 to 200 mm we detected water desorbing from the overlying layers for which we were able to determine a desorption coefficient of 1.45 ¿ 0.5 ¿ 10-3 h-1. After allowing for the effect of desorption, we found that the diffusion coefficient for water vapor through our regolith is 1.74 ¿ 0.70 ¿ 10-4 m2 s-1, in excellent agreement with theoretical values. We thus find that a 1-m thick layer of ice buried below a meter of regolith resembling JSC Mars-1 on Mars at 235 K would last ~800 years.