diff --git a/Reconstruction_simplification_2/doc/Reconstruction_simplification_2/Reconstruction_Simplification_2.txt b/Reconstruction_simplification_2/doc/Reconstruction_simplification_2/Reconstruction_Simplification_2.txt
index 5d013ce1d91..dd529809eac 100644
--- a/Reconstruction_simplification_2/doc/Reconstruction_simplification_2/Reconstruction_Simplification_2.txt
+++ b/Reconstruction_simplification_2/doc/Reconstruction_simplification_2/Reconstruction_Simplification_2.txt
@@ -64,7 +64,7 @@ one can use the run_until function
 \code{.cpp}
   rs2.run_until(20); // perform edge contractions until only 20 vertices are left.
 \endcode
-and specify the number of output vertices one wants to keep as illustrated next.
+and specify the number of output vertices one wants to keep as illustrated in Figure \cgalFigureRef{2D_Reconstruction_Simplification_twenty_vertices}.
 
 \cgalFigureBegin{2D_Reconstruction_Simplification_twenty_vertices,twenty_vertices.png}
 Examples of 20-vertex reconstructions from datasets consisting of 2000, 400 and 200 input points respectively. The examples illustrates the behavior of the algorithm when the input point density decreases. 
diff --git a/Reconstruction_simplification_2/include/CGAL/Reconstruction_simplification_2.h b/Reconstruction_simplification_2/include/CGAL/Reconstruction_simplification_2.h
index 3839e0326fd..d46fe7968ee 100644
--- a/Reconstruction_simplification_2/include/CGAL/Reconstruction_simplification_2.h
+++ b/Reconstruction_simplification_2/include/CGAL/Reconstruction_simplification_2.h
@@ -197,8 +197,8 @@ protected:
 	     \param input_range range of input data.
 	     \param point_map A `ReadablePropertyMap` used to access the input points.
 
-	     \param mass_map A `ReadablePropertyMap` used to access the input points' mass.
-             \param sample_size If `sample_size != 0`, the size of the random sample replaces the exhaustive priority queue.
+	     \param mass_map A `ReadablePropertyMap` used to access the input points' masses.
+             \param sample_size If `sample_size != 0`, the size of the random sample which replaces the exhaustive priority queue.
              \param use_flip If `true` the edge flipping procedure is used to ensure that every edge can be made collapsible.
              \param relocation The number of point relocations that are performed between two edge collapses.
              \param verbose controls how much console output is produced by the algorithm. The values are 0, 1, or > 1.
@@ -1387,10 +1387,10 @@ bool create_pedge(const Edge& edge, Rec_edge_2& pedge) {
 		}
 
 		 /*!
-			Computes a shape, reconstructing the input, by performing `steps` many
+			Computes a shape, reconstructing the input, by performing `steps`
 			edge collapse operators on the output simplex.
 
-			\param steps The number of edge collapse operators performed by the algorithm.
+			\param steps The number of edge collapse operators to be performed.
 		  */
 		void run(const unsigned steps) {
 			double timer = clock();