We give the first {\em fully compressed} representation of a set of $m$ points
on an $n \times n$ grid, taking $H+o(H)$ bits of space, where $H=\lg {n^2
\choose m}$ is the entropy of the set. This representation supports range
counting, range reporting, and point selection queries, with a performance that
is comparable to that of uncompressed structures and that improves upon the
only previous compressed structure. Operating within entropy-bounded space
opens a new line of research on an otherwise well-studied area, and is becoming
extremely important for handling large datasets.