Data fragmentation has recently emerged as a complementary approach to encryption for protecting confidentiality of sensitive associations when storing data at external parties. In this paper, we discuss how the use of indexes, typically associated with the encrypted portion of the data, while desirable for providing effectiveness and efficiency in query execution, can - combined with fragmentation - cause potential leakage of confidential (encrypted or fragmented) information. We illustrate how the exposure to leakage varies depending on the kind of indexes. Such observations can result useful for the design of approaches assessing information exposure and for the definition of safe (free from inferences) indexes in fragmented data.