What impacts what we remember about objects we have just encountered? Influential theories of learning suggest that more active engagement leads to stronger memories than passive observation. However, it is not clear which aspects of interaction lead to stronger memories, nor what kinds of memories are supported by active engagement. Here we conduct several experiments to investigate the impact of assembling an object on subsequent recognition and recall performance. We found that reconstructing a block tower by copying it part-by-part could impair subsequent memory for that tower, compared to passively viewing that tower. By contrast, when participants initially encoded each tower by building it from working memory, their subsequent recall was enhanced relative to when they held the tower in working memory without building it. Together our results suggest a complex relationship between the nature of our interactions with objects and our subsequent memories of them.