Refreshing is one of the mechanisms proposed to maintain information in human working memory. The mechanism is assumed to operate serially, boosting the items of a memory list one after the other. In the current study, we test the most straightforward implementation of serial refreshing, by which refreshing spontaneously reproduces the order of presentation, starting with the first memory item and cycling through the list in a forward fashion, to support short-term memory of a list. Therefore, we examined verbal serial recall performance under different instructed-refreshing schedules that varied in their similarity to cumulative, forward-order refreshing. This was done by manipulating whether instructed refreshing started with the first memory item or not, and whether instructed refreshing proceeded in forward order through the list or not. We expected recall performance to be poorer as participants were required to think of the list items in a way that is more dissimilar to what they would have done spontaneously. However, across four experiments, we observed that recall performance was not drastically affected by the nature of instructed refreshing and thus, we did not find any evidence that cumulative, forward-order refreshing supports serial verbal WM performance.