diff --git a/cogl/cogl-material.c b/cogl/cogl-material.c
index 36716c339..a600e9284 100644
--- a/cogl/cogl-material.c
+++ b/cogl/cogl-material.c
@@ -3899,7 +3899,7 @@ cogl_material_set_blend (CoglHandle handle,
 
 void
 cogl_material_set_blend_constant (CoglHandle handle,
-                                  CoglColor *constant_color)
+                                  const CoglColor *constant_color)
 {
 #ifndef HAVE_COGL_GLES
   CoglMaterial *material = COGL_MATERIAL (handle);
@@ -4590,7 +4590,7 @@ changed:
 void
 cogl_material_set_layer_combine_constant (CoglHandle handle,
 				          int layer_index,
-                                          CoglColor *constant_color)
+                                          const CoglColor *constant_color)
 {
   CoglMaterial          *material = COGL_MATERIAL (handle);
   CoglMaterialLayerState state = COGL_MATERIAL_LAYER_STATE_COMBINE_CONSTANT;
@@ -4671,7 +4671,7 @@ changed:
 void
 cogl_material_set_layer_matrix (CoglHandle handle,
 				int layer_index,
-				CoglMatrix *matrix)
+                                const CoglMatrix *matrix)
 {
   CoglMaterial          *material = COGL_MATERIAL (handle);
   CoglMaterialLayerState state = COGL_MATERIAL_LAYER_STATE_USER_MATRIX;
diff --git a/cogl/cogl-material.h b/cogl/cogl-material.h
index d3cf2273d..f23353663 100644
--- a/cogl/cogl-material.h
+++ b/cogl/cogl-material.h
@@ -593,7 +593,7 @@ cogl_material_set_blend (CoglHandle  material,
  */
 void
 cogl_material_set_blend_constant (CoglHandle material,
-                                  CoglColor *constant_color);
+                                  const CoglColor *constant_color);
 
 /**
  * cogl_material_set_layer:
@@ -742,9 +742,9 @@ cogl_material_set_layer_combine (CoglHandle   material,
  * Since: 1.0
  */
 void
-cogl_material_set_layer_combine_constant (CoglHandle  material,
-                                          int         layer_index,
-                                          CoglColor  *constant);
+cogl_material_set_layer_combine_constant (CoglHandle       material,
+                                          int              layer_index,
+                                          const CoglColor *constant);
 
 /**
  * cogl_material_set_layer_matrix:
@@ -756,9 +756,9 @@ cogl_material_set_layer_combine_constant (CoglHandle  material,
  * and rotate a single layer of a material used to fill your geometry.
  */
 void
-cogl_material_set_layer_matrix (CoglHandle  material,
-				int         layer_index,
-				CoglMatrix *matrix);
+cogl_material_set_layer_matrix (CoglHandle        material,
+                                int               layer_index,
+                                const CoglMatrix *matrix);
 
 /**
  * cogl_material_get_layers:
diff --git a/cogl/cogl-path.c b/cogl/cogl-path.c
index aa64e0baa..426e5ba12 100644
--- a/cogl/cogl-path.c
+++ b/cogl/cogl-path.c
@@ -746,7 +746,7 @@ cogl_path_line (float x_1,
 }
 
 void
-cogl_path_polyline (float *coords,
+cogl_path_polyline (const float *coords,
 	            int num_points)
 {
   int c = 0;
@@ -758,7 +758,7 @@ cogl_path_polyline (float *coords,
 }
 
 void
-cogl_path_polygon (float *coords,
+cogl_path_polygon (const float *coords,
 	           int    num_points)
 {
   cogl_path_polyline (coords, num_points);
diff --git a/cogl/cogl-path.h b/cogl/cogl-path.h
index a0440f226..a4c74c083 100644
--- a/cogl/cogl-path.h
+++ b/cogl/cogl-path.h
@@ -303,8 +303,8 @@ cogl_path_line (float x_1,
  * be constructed.
  **/
 void
-cogl_path_polyline (float *coords,
-                    int    num_points);
+cogl_path_polyline (const float *coords,
+                    int          num_points);
 
 
 /**
@@ -322,8 +322,8 @@ cogl_path_polyline (float *coords,
  * fashion for the rest of the vertices.
  **/
 void
-cogl_path_polygon (float *coords,
-                   int    num_points);
+cogl_path_polygon (const float *coords,
+                   int          num_points);
 
 
 /**