Another variation of cuckoo hashing that has been studied is "cuckoo hashing with a stash". The stash, in this data structure, is an array of a constant number of keys, used to store keys that cannot successfully be inserted into the main hash table of the structure. This modification reduces the failure rate of cuckoo hashing to an inverse-polynomial function with an exponent that can be made arbitrarily large by increasing the stash size. However, larger stashes also mean slower searches for keys that are not present or are in the stash. A stash can be used in combination with more than two hash functions or with blocked cuckoo hashing to achieve both high load factors and small failure rates. The analysis of cuckoo hashing with a stash extends to practical hash functions, not just to the random hash function model commonly used in theoretical analysis of hashing.