diff --git a/Tetrahedral_remeshing/doc/Tetrahedral_remeshing/Doxyfile.in b/Tetrahedral_remeshing/doc/Tetrahedral_remeshing/Doxyfile.in
index a7812ca0fd3..a0a33b4553f 100644
--- a/Tetrahedral_remeshing/doc/Tetrahedral_remeshing/Doxyfile.in
+++ b/Tetrahedral_remeshing/doc/Tetrahedral_remeshing/Doxyfile.in
@@ -6,18 +6,6 @@ EXTRACT_ALL = false
HIDE_UNDOC_CLASSES = true
WARN_IF_UNDOCUMENTED = false
-# macros to be used inside the code
-ALIASES += "cgalNamedParamsBegin=
- Named Parameters
-
"
-ALIASES += "cgalNamedParamsEnd=
"
-ALIASES += "cgalParamBegin{1}=| \ref Remeshing_\1 \"\1\" | "
-ALIASES += "cgalParamEnd= |
"
-
-#macros for NamedParameters.txt
-ALIASES += "cgalNPTableBegin=-
"
-ALIASES += "cgalNPTableEnd=
"
-ALIASES += "cgalNPBegin{1}=| \1 | "
-ALIASES += "cgalNPEnd= |
"
-
EXAMPLE_PATH += ${CGAL_Tetrahedral_remeshing_EXAMPLE_DIR}
EXCLUDE = ${CGAL_PACKAGE_INCLUDE_DIR}/CGAL/Tetrahedral_remeshing/internal
@@ -25,4 +13,4 @@ EXCLUDE = ${CGAL_PACKAGE_INCLUDE_DIR}/CGAL/Tetrahedral_remeshing/internal
#MACRO_EXPANSION = YES
#EXPAND_ONLY_PREDEF = YES
#EXPAND_AS_DEFINED = CGAL_PMP_NP_TEMPLATE_PARAMETERS \
-# CGAL_PMP_NP_CLASS
+# CGAL_PMP_NP_CLASS
diff --git a/Tetrahedral_remeshing/doc/Tetrahedral_remeshing/Tetrahedral_remeshing.txt b/Tetrahedral_remeshing/doc/Tetrahedral_remeshing/Tetrahedral_remeshing.txt
index bca4311f67d..9a2644fbca0 100644
--- a/Tetrahedral_remeshing/doc/Tetrahedral_remeshing/Tetrahedral_remeshing.txt
+++ b/Tetrahedral_remeshing/doc/Tetrahedral_remeshing/Tetrahedral_remeshing.txt
@@ -58,10 +58,7 @@ takes only two required parameters: the input triangulation, and the desired edg
which drives the remeshing process.
\ref BGLNamedParameters are used to deal with optional parameters.
-The page \ref Remeshing_namedparameters provides a description
-of their usage, and of all the available parameters for tuning
-the remeshing process and results.
-
+The page \ref bgl_namedparameters describes their usage.
\section secTetRemeshingExamples Examples
diff --git a/Tetrahedral_remeshing/include/CGAL/tetrahedral_remeshing.h b/Tetrahedral_remeshing/include/CGAL/tetrahedral_remeshing.h
index 7877002a0d5..6809698aacb 100644
--- a/Tetrahedral_remeshing/include/CGAL/tetrahedral_remeshing.h
+++ b/Tetrahedral_remeshing/include/CGAL/tetrahedral_remeshing.h
@@ -85,29 +85,57 @@ namespace CGAL
* among the ones listed below
*
* \cgalNamedParamsBegin
-* \cgalParamBegin{number_of_iterations} the number of iterations for the full
-* sequence of atomic operations
-* performed (listed in the above description)
-* \cgalParamEnd
-* \cgalParamBegin{remesh_boundaries} If `false`, none of the input volume boundaries
-* can be modified.
-* Otherwise, the topology is preserved, but atomic operations can be performed on the
-* surfaces, and along feature polylines, such that boundaries are remeshed.
-* \cgalParamEnd
-* \cgalParamBegin{edge_is_constrained_map} a property map containing the
-* constrained - or - not status of each edge of `tr`. A constrained edge can be split
-* or collapsed, but not flipped.
-* \cgalParamEnd
-* \cgalParamBegin{facet_is_constrained_map} a property map containing the
-* constrained - or - not status of each facet of `tr`. A constrained facet can be split
-* or collapsed, but not flipped.
-* \cgalParamEnd
-* \cgalParamBegin{cell_is_selected_map} a property map containing the
-* selected - or - not status for each cell of `tr` for remeshing.
-* Only selected cells are modified (and possibly their neighbors if surfaces are
-* modified) by remeshing.
-* By default, all cells with a non-zero `Subdomain_index` are selected.
-* \cgalParamEnd
+* \cgalParamNBegin{number_of_iterations}
+* \cgalParamDescription{the number of iterations for the full sequence of atomic operations
+* performed (listed in the above description)}
+* \cgalParamType{unsigned int}
+* \cgalParamDefault{`1`}
+* \cgalParamNEnd
+*
+* \cgalParamNBegin{remesh_boundaries}
+* \cgalParamDescription{If `false`, none of the input volume boundaries can be modified.
+* Otherwise, the topology is preserved, but atomic operations
+* can be performed on the surfaces, and along feature polylines,
+* such that boundaries are remeshed.}
+* \cgalParamType{Boolean}
+* \cgalParamDefault{`true`}
+* \cgalParamExtra{Boundaries are between the exterior and the interior,
+* between two subdomains, between the areas selected or not for remeshing
+* (cf \ref Remeshing_cell_is_selected_map), or defined
+* by \ref Remeshing_edge_is_constrained_map
+* and \ref Remeshing_facet_is_constrained_map.}
+* \cgalParamNEnd
+*
+* \cgalParamNBegin{edge_is_constrained_map}
+* \cgalParamDescription{a property map containing the constrained-or-not status of each edge of `tr`.}
+* \cgalParamType{a class model of `ReadWritePropertyMap` with `std::pair`
+* as key type and `bool` as value type. It must be default constructible.}
+* \cgalParamDefault{a default property map where no edge is constrained}
+* \cgalParamExtra{A constrained edge can be split or collapsed, but not flipped.}
+* \cgalParamExtra{The pairs must be ordered to ensure consistency.}
+* \cgalParamExtra{During the meshing process, the set of constrained edges evolves consistently
+* with edge splits and collapses, so the property map must be writable.}
+* \cgalParamNEnd
+*
+* \cgalParamNBegin{facet_is_constrained_map}
+* \cgalParamDescription{a property map containing the constrained-or-not status of each facet of `tr`.}
+* \cgalParamType{a class model of `ReadablePropertyMap` with `Triangulation_3::Facet`
+* as key type and `bool` as value type. It must be default constructible.}
+* \cgalParamDefault{a default property map where no facet is constrained}
+* \cgalParamExtra{A constrained facet can be split or collapsed, but not flipped.}
+* \cgalParamExtra{This map, contrary to the others, is not updated throughout the remeshing process.}
+* \cgalParamNEnd
+*
+* \cgalParamNBegin{cell_is_selected_map}
+* \cgalParamDescription{a property map containing the selected - or - not status for each cell of `tr` for remeshing.
+* Only selected cells are modified (and possibly their neighbors if surfaces are modified) by remeshing.}
+* \cgalParamType{a class model of `ReadWritePropertyMap` with `Triangulation_3::Cell_handle`
+* as key type and `bool` as value type. It must be default constructible.}
+* \cgalParamDefault{a default property map where all cells of the domain
+* (i.e. with a non-zero `Subdomain_index`) are selected.}
+* \cgalParamExtra{During the meshing process, the set of selected cells evolves consistently with
+* the atomic operations that are performed, so the property map must be writable.}
+* \cgalParamNEnd
* \cgalNamedParamsEnd
*
* \sa `CGAL::Tetrahedral_remeshing::Remeshing_triangulation_3`