Field measurements show that estimated sediment deposition rate decreases as a power law function of the measurement interval. This apparent decrease in sediment deposition has been attributed to completeness of the sedimentary record; the effect arises because of incorporation of longer hiatuses in deposition as averaging time is increased. We demonstrate that a heavy-tailed distribution of periods of nondeposition (hiatuses) produces this phenomenon and that observed accumulation rate decreases as tγ−1, over multiple orders of magnitude, where 0 < γ ≤ 1 is the parameter describing the tail of the distribution of quiescent period length. By using continuous time random walks and limit theory, we can estimate the actual average deposition rate from observations of the surface location over time. If geologic and geometric constraints place an upper limit on the length of hiatuses, then average accumulation rates approach a constant value at very long times. Our model suggests an alternative explanation for the apparent increase in global sediment accumulation rates over the last 5 million years.