We consider the problem of finding an element of a given rank in a totally ordered set given in a read-only array, using limited
extra storage cells. We give new algorithms for various ranges of extra space. Our upper bounds improve the previously known
bounds in the range of space s such that s is o(lg2
n) and s ≥ clg lg n/lg lg lg n for some constant c. We also give faster algorithms to find small ranks.