Factors affecting the fragmentation pattern of cell-free DNA (e.g., plasma DNA) and the applications, including those in molecular diagnostics, of the analysis of cell-free DNA fragmentation patterns are described. Various applications can use a property of a fragmentation pattern to determine a proportional contribution of a particular tissue type, to determine a genotype of a particular tissue type (e.g., fetal tissue in a maternal sample or tumor tissue in a sample from a cancer patient), and/or to identify preferred ending positions for a particular tissue type, which may then be used to determine a proportional contribution of a particular tissue type.