Two highly studied memory functions are memory for associations (items presented in pairs, such as SALT-PEPPER) and memory for order (a list of items whose order matters, such as a telephone number). Order- and association-memory are at the root of many forms of behaviour, from wayfinding, to language, to remembering people's names. Most researchers have investigated memory for order separately from memory for associations. Exceptions to this, associative-chaining models build an ordered list from associations between pairs of items, quite literally understanding association- and order-memory together. Alternatively, positional-coding models have been used to explain order-memory as a completely distinct function from association-memory. Both classes of model have found empirical support and both have faced serious challenges. I argue that models that combine both associative chaining and positional coding are needed. One such hybrid model, which relies on brain-activity rhythms, is promising, but remains to be tested rigourously. I consider two relatively understudied memory behaviours that demand a combination of order- and association-information: memory for the order of items within associations (is it William James or James William?) and judgments of relative order (who left the party earlier, Hermann or William?). Findings from these underexplored procedures are already difficult to reconcile with existing association-memory and order-memory models. Further work with such intermediate experimental paradigms has the potential to provide powerful findings to constrain and guide models into the future, with the aim of explaining a large range of memory functions, encompassing both association- and order-memory.