An item bundle is a set of items where theoretical arguments imply that the assumptions of local independence may be violated. In educational tests, this may be because items share a common stimulus material, e.g. a text passage or a graph. In self-reported health scales measuring physical functioning, items may be expected to be locally dependent if they refer to a specific body part or action. This paper describes and compares two different Rasch models for item bundles, where polytomous super items summarizing responses to bundle items fit Rasch models, and where the total score over all locally independent or dependent items is statistically sufficient for the person parameter of the model. The paper will show that measurements of a latent trait by the two models are equivalent and that items fitting one of these models will also fit the other model.