diff --git a/Packages/Spatial_searching/doc_tex/Spatial_searching/intro.tex b/Packages/Spatial_searching/doc_tex/Spatial_searching/intro.tex
index 5133bec9499..60ff6216442 100755
--- a/Packages/Spatial_searching/doc_tex/Spatial_searching/intro.tex
+++ b/Packages/Spatial_searching/doc_tex/Spatial_searching/intro.tex
@@ -2,9 +2,9 @@
 
 \section{Introduction}
 
-The {\bf spatial searching} package implements
-exact and approximate distance browsing
-by providing implementations of algorithms supporting
+The spatial searching package implements exact and approximate
+distance browsing by providing implementations of algorithms
+supporting
 
 \begin{itemize} 
 
@@ -90,7 +90,7 @@ neighbor must not be smaller than $r/(1+\epsilon)$.  Obviously, for
 $\epsilon=0$ we get the exact result, and the larger $\epsilon$ is,
 the less exact the result.
 
-\subsection{Range searching}
+\subsection{Range Searching}
 
 {\bf Exact range searching} and {\bf approximate range searching} is
 supported using exact or fuzzy $d$-dimensional objects enclosing a
@@ -218,7 +218,7 @@ coordinates.
 \ccIncludeExampleCode{../../examples/Spatial_searching/Fuzzy_range_query.C}
 
 
-\subsection{Example of Distance Browsing}
+\subsection{Example of Incremental Searching}
 
 This example program illustrates distance browsing for $4$-dimensional
 points with a positive first coordinate using orthogonal priority
@@ -241,7 +241,7 @@ in this file as well.
 
 \ccIncludeExampleCode{../../examples/Spatial_searching/User_defined_point_and_distance.C}
 
-\section{Software design}
+\section{Software Design}
 
 \begin{ccTexOnly}
 \begin{figure}[t]
@@ -331,7 +331,7 @@ as implemented by \ccc{CGAL::Plane_separator<NT>}.
 \ccc{CGAL::Sliding_Fair<SpatialPoint, PointContainer, SpatialSeparator>}.
 
 \item
-\ccc{TreeTraits} denoting a traits class for the construction of a tree.
+\ccc{PointTraits} denoting a traits class for the construction of a tree.
 \ccc{CGAL::Kd_tree_traits_point< SpatialPoint, Splitter >} provides an implementation. 
 
 \item
@@ -360,18 +360,18 @@ a weighted Minkowski metric.
 
 \item
 \ccc{SpatialTree} denoting a tree supporting spatial searching 
-\ccc{CGAL::Kd_tree<TreeTraits>} provides an implementation of $k$-$d$ trees.
+\ccc{CGAL::Kd_tree<PointTraits>} provides an implementation of $k$-$d$ trees.
 
 \end{itemize}
 
-\subsection{Neighbor search}
+\subsection{Neighbor Search}
 
 The four classes implementing neighbor searching algorithms are
 
 \begin{itemize}
 
 \item
-The class \ccc{CGAL::General_standard_search<TreeTraits, Distance, QueryItem, SpatialTree>} 
+The class \ccc{CGAL::K_neighbor_search<PointTraits, Distance, QueryItem, SpatialTree>} 
 implementing the standard search strategy for general distances
 like the Manhattan distance for iso-rectangles.
 Requires no use of extended nodes in the $k$-$d$ tree and supports only $k$
@@ -379,21 +379,22 @@ neighbor searching for queries defined by points or spatial objects.
 
 
 \item
-The class \ccc{CGAL::General_priority_search<TreeTraits, GeneralDistance, QueryItem, SpatialTree>} implementing the priority search 
-strategy for general distances
-like the Manhattan distance for iso-rectangles.
-Requires no use of extended nodes in the $k$-$d$ tree and supports incremental
-neighbor searching and distance browsing for queries defined by points or spatial objects.
+The class \ccc{CGAL::Incremental_neighbor_search<PointTraits,
+GeneralDistance, QueryItem, SpatialTree>} implementing the incremental
+search strategy for general distances like the Manhattan distance for
+iso-rectangles.  Requires no use of extended nodes in the $k$-$d$ tree
+and supports incremental neighbor searching and distance browsing for
+queries defined by points or spatial objects.
 
 \item
-The class \ccc{CGAL::Orthogonal_standard_search<TreeTraits, OrthogonalDistance, SpatialTree>} implementing the standard search strategy for 
-orthogonal distances
+The class \ccc{CGAL::Orthogonal_k_neighbor_search<PointTraits, OrthogonalDistance, SpatialTree>} 
+implementing the standard search strategy for orthogonal distances
 like a weighted Minkowski distance. Requires the use of extended nodes in the $k$-$d$ tree and supports 
 only $k$ neighbor searching for point queries.
 
 \item
-The class \ccc{Orthogonal_priority_search<TreeTraits, GeneralDistance, QueryItem, SpatialTree>} implementing the priority search strategy for general 
-distances
+The class \ccc{Orthogonal_incremental_neighbor_search<PointTraits, GeneralDistance, QueryItem, SpatialTree>} 
+implementing the priority search strategy for general distances
 like a weighted Minkowski distance. Requires the use of extended nodes in the $k$-$d$ tree and supports incremental
 neighbor searching and distance browsing for point queries.
 
@@ -410,7 +411,7 @@ methods to compute bounding boxes
 of point sets and methods to split iso-rectangles.
 
 \item
-The class \ccc{CGAL::Kd_tree_node<TreeTraits>} implementing $k$-$d$ tree nodes.
+The class \ccc{CGAL::Kd_tree_node<PointTraits>} implementing $k$-$d$ tree nodes.
 
 \end{itemize}
 
@@ -511,10 +512,9 @@ generate empty cells.
 \section{Backward compability with the Kd-trees package}
 \label{Spatial_searching:Backward_compability_Kd-trees}
 
-In release 2.3 of CGAL
-$k$-$d$ trees have been implemented by the class \ccc{CGAL::Kdtree_d<TreeTraits>}, 
-that is parameterized with one of the
-traits classes 
+In release 2.3 of \cgal\ $k$-$d$ trees have been implemented by the
+class \ccc{CGAL::Kdtree_d<PointTraits>}, that is parameterized with
+one of the traits classes
 
 \begin{itemize}
 
diff --git a/Packages/Spatial_searching/doc_tex/basic/Spatial_searching/intro.tex b/Packages/Spatial_searching/doc_tex/basic/Spatial_searching/intro.tex
index 5133bec9499..60ff6216442 100755
--- a/Packages/Spatial_searching/doc_tex/basic/Spatial_searching/intro.tex
+++ b/Packages/Spatial_searching/doc_tex/basic/Spatial_searching/intro.tex
@@ -2,9 +2,9 @@
 
 \section{Introduction}
 
-The {\bf spatial searching} package implements
-exact and approximate distance browsing
-by providing implementations of algorithms supporting
+The spatial searching package implements exact and approximate
+distance browsing by providing implementations of algorithms
+supporting
 
 \begin{itemize} 
 
@@ -90,7 +90,7 @@ neighbor must not be smaller than $r/(1+\epsilon)$.  Obviously, for
 $\epsilon=0$ we get the exact result, and the larger $\epsilon$ is,
 the less exact the result.
 
-\subsection{Range searching}
+\subsection{Range Searching}
 
 {\bf Exact range searching} and {\bf approximate range searching} is
 supported using exact or fuzzy $d$-dimensional objects enclosing a
@@ -218,7 +218,7 @@ coordinates.
 \ccIncludeExampleCode{../../examples/Spatial_searching/Fuzzy_range_query.C}
 
 
-\subsection{Example of Distance Browsing}
+\subsection{Example of Incremental Searching}
 
 This example program illustrates distance browsing for $4$-dimensional
 points with a positive first coordinate using orthogonal priority
@@ -241,7 +241,7 @@ in this file as well.
 
 \ccIncludeExampleCode{../../examples/Spatial_searching/User_defined_point_and_distance.C}
 
-\section{Software design}
+\section{Software Design}
 
 \begin{ccTexOnly}
 \begin{figure}[t]
@@ -331,7 +331,7 @@ as implemented by \ccc{CGAL::Plane_separator<NT>}.
 \ccc{CGAL::Sliding_Fair<SpatialPoint, PointContainer, SpatialSeparator>}.
 
 \item
-\ccc{TreeTraits} denoting a traits class for the construction of a tree.
+\ccc{PointTraits} denoting a traits class for the construction of a tree.
 \ccc{CGAL::Kd_tree_traits_point< SpatialPoint, Splitter >} provides an implementation. 
 
 \item
@@ -360,18 +360,18 @@ a weighted Minkowski metric.
 
 \item
 \ccc{SpatialTree} denoting a tree supporting spatial searching 
-\ccc{CGAL::Kd_tree<TreeTraits>} provides an implementation of $k$-$d$ trees.
+\ccc{CGAL::Kd_tree<PointTraits>} provides an implementation of $k$-$d$ trees.
 
 \end{itemize}
 
-\subsection{Neighbor search}
+\subsection{Neighbor Search}
 
 The four classes implementing neighbor searching algorithms are
 
 \begin{itemize}
 
 \item
-The class \ccc{CGAL::General_standard_search<TreeTraits, Distance, QueryItem, SpatialTree>} 
+The class \ccc{CGAL::K_neighbor_search<PointTraits, Distance, QueryItem, SpatialTree>} 
 implementing the standard search strategy for general distances
 like the Manhattan distance for iso-rectangles.
 Requires no use of extended nodes in the $k$-$d$ tree and supports only $k$
@@ -379,21 +379,22 @@ neighbor searching for queries defined by points or spatial objects.
 
 
 \item
-The class \ccc{CGAL::General_priority_search<TreeTraits, GeneralDistance, QueryItem, SpatialTree>} implementing the priority search 
-strategy for general distances
-like the Manhattan distance for iso-rectangles.
-Requires no use of extended nodes in the $k$-$d$ tree and supports incremental
-neighbor searching and distance browsing for queries defined by points or spatial objects.
+The class \ccc{CGAL::Incremental_neighbor_search<PointTraits,
+GeneralDistance, QueryItem, SpatialTree>} implementing the incremental
+search strategy for general distances like the Manhattan distance for
+iso-rectangles.  Requires no use of extended nodes in the $k$-$d$ tree
+and supports incremental neighbor searching and distance browsing for
+queries defined by points or spatial objects.
 
 \item
-The class \ccc{CGAL::Orthogonal_standard_search<TreeTraits, OrthogonalDistance, SpatialTree>} implementing the standard search strategy for 
-orthogonal distances
+The class \ccc{CGAL::Orthogonal_k_neighbor_search<PointTraits, OrthogonalDistance, SpatialTree>} 
+implementing the standard search strategy for orthogonal distances
 like a weighted Minkowski distance. Requires the use of extended nodes in the $k$-$d$ tree and supports 
 only $k$ neighbor searching for point queries.
 
 \item
-The class \ccc{Orthogonal_priority_search<TreeTraits, GeneralDistance, QueryItem, SpatialTree>} implementing the priority search strategy for general 
-distances
+The class \ccc{Orthogonal_incremental_neighbor_search<PointTraits, GeneralDistance, QueryItem, SpatialTree>} 
+implementing the priority search strategy for general distances
 like a weighted Minkowski distance. Requires the use of extended nodes in the $k$-$d$ tree and supports incremental
 neighbor searching and distance browsing for point queries.
 
@@ -410,7 +411,7 @@ methods to compute bounding boxes
 of point sets and methods to split iso-rectangles.
 
 \item
-The class \ccc{CGAL::Kd_tree_node<TreeTraits>} implementing $k$-$d$ tree nodes.
+The class \ccc{CGAL::Kd_tree_node<PointTraits>} implementing $k$-$d$ tree nodes.
 
 \end{itemize}
 
@@ -511,10 +512,9 @@ generate empty cells.
 \section{Backward compability with the Kd-trees package}
 \label{Spatial_searching:Backward_compability_Kd-trees}
 
-In release 2.3 of CGAL
-$k$-$d$ trees have been implemented by the class \ccc{CGAL::Kdtree_d<TreeTraits>}, 
-that is parameterized with one of the
-traits classes 
+In release 2.3 of \cgal\ $k$-$d$ trees have been implemented by the
+class \ccc{CGAL::Kdtree_d<PointTraits>}, that is parameterized with
+one of the traits classes
 
 \begin{itemize}