We present a new data structure to index strings that is very similar to a suffix tree. The new structure indexes the factors of a string whose length does not exceed k, and only those. We call such structure the at most k-deep factor tree, or k-factor tree for short. Time and space complexities for constructing the tree are linear in the length of the string. The construction is on-line. Compared to a suffix tree, the k-factor tree offers a substantial gain in terms of space complexity for small values of k, as well as a gain in time when used for enumerating all occurrences of a pattern in a text indexed by such a k-factor tree.