However, for small trees the overhead associated with vEB trees is enormous: on the order of formula_5. This is one reason why they are not popular in practice. One way of addressing this limitation is to use only a fixed number of bits per level, which results in a trie. Alternatively, each table may be replaced by a hash table, reducing the space to (where is the number of elements stored in the data structure) at the expense of making the data structure randomized. Other structures, including y-fast tries and x-fast tries have been proposed that have comparable update and query times and also use randomized hash tables to reduce the space to or .