  In this paper we study two geometric data structure problems in the special
case when input objects or queries are fat rectangles. We show that in this
case a significant improvement compared to the general case can be achieved.
  We describe data structures that answer two- and three-dimensional orthogonal
range reporting queries in the case when the query range is a \emph{fat}
rectangle. Our two-dimensional data structure uses $O(n)$ words and supports
queries in $O(\log\log U +k)$ time, where $n$ is the number of points in the
data structure, $U$ is the size of the universe and $k$ is the number of points
in the query range. Our three-dimensional data structure needs
$O(n\log^{\varepsilon}U)$ words of space and answers queries in $O(\log \log U
+ k)$ time. We also consider the rectangle stabbing problem on a set of
three-dimensional fat rectangles. Our data structure uses $O(n)$ space and
answers stabbing queries in $O(\log U\log\log U +k)$ time.
