A central claim shared by most recent models of short-term memory (STM) is that item knowledge is coded independently from order in long-term memory (LTM; e.g., the letter A is coded by the same representational unit whether it occurs at the start or end of a sequence). Serial order is computed by dynamically binding these item codes to a separate representation of order. By contrast, Botvinick and Plaut (2006) developed a parallel distributed processing (PDP) model of STM that codes for item-order information conjunctively, such that the same letter in different positions is coded differently in LTM. Their model supports a wide range of memory phenomena, and critically, STM is better for lists that include high, as opposed to low, sequential dependencies (e.g., bigram effects). Models with context-independent item representations do not currently account for sequential effects. However, we show that their PDP model is too sensitive to these effects. A modified version of the model does better but still fails in important respects. The successes and failures can be attributed to a fundamental constraint associated with context-dependent representations. We question the viability of conjunctive coding schemes to support STM and take these findings as problematic for the PDP approach to cognition more generally. (Contains 3 footnotes and 7 figures.)