diff --git a/doc/texinfo/gmsh.texi b/doc/texinfo/gmsh.texi
index 59cff15e061fabe8ec11330c22ef6b42c1178770..353792c197fcf7ae6fec45cf995d77dbaf10110f 100644
--- a/doc/texinfo/gmsh.texi
+++ b/doc/texinfo/gmsh.texi
@@ -491,12 +491,6 @@ surfaces in Gmsh's scripting language (however you can import STEP or
 IGES models with such features when Gmsh is built with OpenCascade
 support);
 @item
-Gmsh is not primarily a structured mesh generator: no automatic
-quadrilateral or hexahedral meshing algorithm is provided. If you want
-quadrangles, you have to use transfinite or extruded meshes or recombine
-unstructured triangular meshes. For hexahedra, your only choice is
-transfinite or extruded meshes;
-@item
 Gmsh is not a multi-bloc generator: all meshes produced by Gmsh are
 conforming in the sense of finite element meshes;
 @item
@@ -2102,20 +2096,30 @@ GUI, is give in  @ref{Geometry options list}.
 @cindex Mesh, module
 @cindex Module, Mesh
 
-Gmsh's mesh module regroups several 1D, 2D and 3D mesh algorithms, all
-producing grids conforming in the sense of finite elements (@pxref{Mesh}).
-
-The 2D @emph{unstructured} algorithms generate triangles or both triangles
-and quadrangles (when @code{Recombine Surface} is used: see
-@ref{Miscellaneous mesh commands}). The 3D unstructured algorithms only
-generate tetrahedra.
+Gmsh's mesh module regroups several 1D, 2D and 3D meshing algorithms,
+all producing grids conforming in the sense of finite elements
+(@pxref{Mesh}):
 
+@itemize @bullet
+@item
+The 2D @emph{unstructured} algorithms generate triangles or both
+triangles and quadrangles (when @code{Recombine Surface} is used: see
+@ref{Miscellaneous mesh commands}). The 3D @emph{unstructured}
+algorithms generate tetrahedra.
+@item
 The 2D @emph{structured} algorithms (transfinite and extrusion) generate
 triangles by default, but quadrangles can be obtained by using the
 @code{Recombine} commands (see @ref{Structured grids}, and
-@ref{Miscellaneous mesh commands}). The 3D structured algorithms
+@ref{Miscellaneous mesh commands}). The 3D @emph{structured} algorithms
 generate tetrahedra, hexahedra, prisms and pyramids, depending on the
 type of the surface meshes they are based on.
+@end itemize
+
+All meshes can be subdivided to generate fully quadrangular or fully
+hexahedral meshes with the @code{Mesh.SubdivisionAlgorihm} option
+(@pxref{Mesh options list}). However, beware that the quality of
+subdivided elements initially generated with an @emph{unstructured}
+algorithm can be quite poor.
 
 @c todo: explain what happens if we have a degenerate geometry (incorrect
 @c holes with surfaces in contact with the exterior shell, intersecting
diff --git a/doc/texinfo/opt_mesh.texi b/doc/texinfo/opt_mesh.texi
index 4bd5718b3b0e9ee34b8a3b5ec6d25b56bf823ee1..285ae0d0d618d64412402ddcfe015119b793a03a 100644
--- a/doc/texinfo/opt_mesh.texi
+++ b/doc/texinfo/opt_mesh.texi
@@ -409,11 +409,6 @@ Number of refinement steps in the MeshAdapt-based 2D algorithms@*
 Default value: @code{10}@*
 Saved in: @code{General.OptionsFileName}
 
-@item Mesh.RecombineAlgo
-Recombine algorithm (1=mixed triangles-quadrangles, 2=all quadrangles)@*
-Default value: @code{1}@*
-Saved in: @code{General.OptionsFileName}
-
 @item Mesh.ReverseAllNormals
 Reverse all the mesh normals (for display)@*
 Default value: @code{0}@*
@@ -469,6 +464,11 @@ Smooth the mesh normals?@*
 Default value: @code{0}@*
 Saved in: @code{General.OptionsFileName}
 
+@item Mesh.SubdivisionAlgorithm
+Mesh subdivision algorithm (0=none, 1=all quadrangles, 2=all hexahedra)@*
+Default value: @code{0}@*
+Saved in: @code{General.OptionsFileName}
+
 @item Mesh.SurfaceEdges
 Display edges of surface mesh?@*
 Default value: @code{1}@*