  We consider the problem of preprocessing $N$ points in 2D, each endowed with
a priority, to answer the following queries: given a axis-parallel rectangle,
determine the point with the largest priority in the rectangle. Using the ideas
of the \emph{effective entropy} of range maxima queries and \emph{succinct
indices} for range maxima queries, we obtain a structure that uses O(N) words
and answers the above query in $O(\log N \log \log N)$ time. This is a direct
improvement of Chazelle's result from FOCS 1985 for this problem -- Chazelle
required $O(N/\epsilon)$ words to answer queries in $O((\log N)^{1+\epsilon})$
time for any constant $\epsilon > 0$.
