Let the position of a list element in a list be the number of elements preceding it plus one. An indexed list supports the following operations on a list: Insert; delete; return the position of an element; and return the element at a certain position. The order in which the elements appear in the list is completely determined by where the insertions take place; we do not require the presence of any keys that induce the ordering.
We consider approximate indexed lists, and show that a tiny relaxation in precision of the query operations allows a considerable improvement in time complexity. The new data structure has applications in two other problems; namely, list labeling and subset rank.