Palimpsest glacial dispersal trains are residual trains that are produced when the lithic components of an earlier dispersal trains are incompletely re-entrained by a subsequent glacial movement in a different direction. As evidence for multiple ice-flow directions comes from an ever growing number of regions, palimpsest trains increasingly appear as common features of glacial dispersal patterns produced by Quaternary ice sheets. The major characteristics of these trains, particularly their trend and outline, are predominantly related to an earlier glacial movement and only partly related to the glacial movement that produced the till sheet in which they occur. Palimpsest dispersal trains owe their characteristics to the cumulative effects of two or more succeeding ice-flow directions. The concept of palimpsest trains leads not only to a better understanding of the factors which control glacial dispersal patterns but also to an integrated classification of dispersal trains. The three main types of glacial dispersal trains, ribbon-shaped, fan-shaped and amoeboid, owe their characteristics features to the direction, number and succession of former glacial movements. The concept of palimpsest dispersal trains is supported by an empirical glacial dispersal model which do not only constrains the conditions under which these trains may form but also identifies two key factors of subglacial clastic dispersal: (1) the travel distance of basal ice and (2) the rate of subglacial erosion. The basis of this glacial dispersal model is a corollary of Krumbein's exponential decay model: the concentration of lithic components of a rock type in subglacial debris increases exponentially until its distal contact is crossed, at which point the exponential increase of lithic components of rock types lying downglacier will cause the concentration of lithic components of the first rock type to decrease exponentially. The proposed model carries out multiple iterations during each of which compositional data obtained by the previous iteration are redistributed through an exponential decay function. Our work shows that not only is it important to know the sequences of ice-flow directions which occurred in glaciated terrains but also to recognize that older glacial movements are most likely to have residual effects on dispersal patterns produced during subsequent glacial movements. The recognition of palimpsest dispersal trains provides a new tool to better assess these residual effects on regional geochemical patterns in glacial sediments and thus to adjust drift prospecting strategies.