A mode of a multiset $S$ is an element $a \in S$ of maximum multiplicity;
that is, $a$ occurs at least as frequently as any other element in $S$. Given a
list $A[1:n]$ of $n$ items, we consider the problem of constructing a data
structure that efficiently answers range mode queries on $A$. Each query
consists of an input pair of indices $(i, j)$ for which a mode of $A[i:j]$ must
be returned. We present an $O(n^{2-2\epsilon})$-space static data structure
that supports range mode queries in $O(n^\epsilon)$ time in the worst case, for
any fixed $\epsilon \in [0,1/2]$.