The aggregation of lower-level units into higher-level wholes seems to be correlated, in evolution, with two effects: 1) The loss of internal structure or complexity in the lower-level units; and 2) the emergence of complexity at an intermediate level. In effect, structural complexity is transferred from a lower level to a higher one. Thus, for example, cells in multicellular organisms seem to have fewer parts than free-living cells (protists), but multicellular organisms have intermediate-level parts, i.e., tissues and organs. At a higher level, the individuals in animal colonies seem to have fewer parts than their more solitary relatives, but individuals in colonies often collaborate to perform functions, again producing intermediate-level parts. These patterns have had little empirical support, so far, because operationalizing the key variable i.e., parts has been difficult. In this talk, I show how operationalization was achieved in a recent effort to document a part of the pattern, specifically the loss of parts in cell. Finally, this transfer of complexity across levels may be explained by a simple and fairly general logic, based on natural selection. If the explanation is right, the possibility arises that the pattern may be widespread, occurring in non-biological systems subject to similar constraints.