High precision uranium isotope measurements of marine clastic sediments are used to measure the transport and storage time of sediment from source to site of deposition. The approach is demonstrated on fine-grained, late Pleistocene deep-sea sediments from Ocean Drilling Program Site 984A on the Bjorn Drift in the North Atlantic. The sediments are siliciclastic with up to 30 percent carbonate, and dated by sigma 18O of benthic foraminifera. Nd and Sr isotopes indicate that provenance has oscillated between a proximal source during the last three interglacial periods volcanic rocks from Iceland and a distal continental source during glacial periods. An unexpected finding is that the 234U/238U ratios of the silicate portion of the sediment, isolated by leaching with hydrochloric acid, are significantly less than the secular equilibrium value and show large and systematic variations that are correlated with glacial cycles and sediment provenance. The 234U depletions are inferred to be due to alpha-recoil loss of 234Th, and are used to calculate "comminution ages" of the sediment -- the time elapsed between the generation of the small (