diff --git a/doomsday/client/include/world/blockmap.h b/doomsday/client/include/world/blockmap.h
index 12016eee1e..05d2014a8d 100644
--- a/doomsday/client/include/world/blockmap.h
+++ b/doomsday/client/include/world/blockmap.h
@@ -122,9 +122,9 @@ class Blockmap
 
     bool unlink(CellBlock const &cellBlock, void *elem);
 
-    int iterate(Cell const &cell, int (*callback) (void *elem, void *context), void *context);
+    int iterate(Cell const &cell, int (*callback) (void *elem, void *context), void *context) const;
 
-    int iterate(CellBlock const &cellBlock, int (*callback) (void *elem, void *context), void *context);
+    int iterate(CellBlock const &cellBlock, int (*callback) (void *elem, void *context), void *context) const;
 
     /**
      * Retrieve an immutable pointer to the underlying Gridmap instance
diff --git a/doomsday/client/include/world/map.h b/doomsday/client/include/world/map.h
index c226c11c03..adfaec5526 100644
--- a/doomsday/client/include/world/map.h
+++ b/doomsday/client/include/world/map.h
@@ -284,22 +284,22 @@ class Map
     /**
      * Provides access to the mobj blockmap.
      */
-    Blockmap /*const*/ *mobjBlockmap() const;
+    Blockmap const *mobjBlockmap() const;
 
     /**
      * Provides access to the polyobj blockmap.
      */
-    Blockmap /*const*/ *polyobjBlockmap() const;
+    Blockmap const *polyobjBlockmap() const;
 
     /**
      * Provides access to the line blockmap.
      */
-    Blockmap /*const*/ *lineBlockmap() const;
+    Blockmap const *lineBlockmap() const;
 
     /**
      * Provides access to the BSP leaf blockmap.
      */
-    Blockmap /*const*/ *bspLeafBlockmap() const;
+    Blockmap const *bspLeafBlockmap() const;
 
     int mobjsBoxIterator(AABoxd const &box,
         int (*callback) (struct mobj_s *, void *), void *parameters = 0) const;
diff --git a/doomsday/client/src/render/blockmapvisual.cpp b/doomsday/client/src/render/blockmapvisual.cpp
index bec68cb37a..78ffca7224 100644
--- a/doomsday/client/src/render/blockmapvisual.cpp
+++ b/doomsday/client/src/render/blockmapvisual.cpp
@@ -148,7 +148,7 @@ static int rendBspLeaf(BspLeaf *bspLeaf, void * /*parameters*/)
     return false; // Continue iteration.
 }
 
-static int rendCellLines(Blockmap &bmap, Blockmap::Cell const &cell, void *parameters)
+static int rendCellLines(Blockmap const &bmap, Blockmap::Cell const &cell, void *parameters)
 {
     glBegin(GL_LINES);
         bmap.iterate(cell, (int (*)(void*,void*)) rendLine, parameters);
@@ -172,7 +172,7 @@ static int rendCellPolyobjLines(void *object, void *parameters)
     return false; // Continue iteration.
 }
 
-static int rendCellPolyobjs(Blockmap &bmap, Blockmap::Cell const &cell, void *parameters)
+static int rendCellPolyobjs(Blockmap const &bmap, Blockmap::Cell const &cell, void *parameters)
 {
     glBegin(GL_LINES);
         bmap.iterate(cell, (int (*)(void*,void*)) rendCellPolyobjLines, parameters);
@@ -180,7 +180,7 @@ static int rendCellPolyobjs(Blockmap &bmap, Blockmap::Cell const &cell, void *pa
     return false; // Continue iteration.
 }
 
-static int rendCellMobjs(Blockmap &bmap, Blockmap::Cell const &cell, void *parameters)
+static int rendCellMobjs(Blockmap const &bmap, Blockmap::Cell const &cell, void *parameters)
 {
     glBegin(GL_QUADS);
         bmap.iterate(cell, (int (*)(void*,void*)) rendMobj, parameters);
@@ -188,13 +188,13 @@ static int rendCellMobjs(Blockmap &bmap, Blockmap::Cell const &cell, void *param
     return false; // Continue iteration.
 }
 
-static int rendCellBspLeafs(Blockmap &bmap, Blockmap::Cell const &cell, void *parameters)
+static int rendCellBspLeafs(Blockmap const &bmap, Blockmap::Cell const &cell, void *parameters)
 {
     bmap.iterate(cell, (int (*)(void*,void*)) rendBspLeaf, parameters);
     return false; // Continue iteration.
 }
 
-static void rendBlockmapBackground(Blockmap &bmap)
+static void rendBlockmapBackground(Blockmap const &bmap)
 {
     Blockmap::Cell const &bmapDimensions = bmap.dimensions();
 
@@ -266,7 +266,7 @@ static void drawCellInfo(Point2Raw const *_origin, char const *info)
     glDisable(GL_TEXTURE_2D);
 }
 
-static void drawBlockmapInfo(Point2Raw const *_origin, Blockmap *blockmap)
+static void drawBlockmapInfo(Point2Raw const *_origin, Blockmap const *blockmap)
 {
     DENG_ASSERT(blockmap != 0);
 
@@ -314,7 +314,7 @@ static void drawBlockmapInfo(Point2Raw const *_origin, Blockmap *blockmap)
     glDisable(GL_TEXTURE_2D);
 }
 
-static void drawCellInfoBox(Blockmap *blockmap, Point2Raw const *origin,
+static void drawCellInfoBox(Blockmap const *blockmap, Point2Raw const *origin,
     char const *objectTypeName, Blockmap::Cell const &cell)
 {
     uint count = blockmap->cellElementCount(cell);
@@ -329,8 +329,8 @@ static void drawCellInfoBox(Blockmap *blockmap, Point2Raw const *origin,
  * @param followMobj  Mobj to center/focus the visual on. Can be @c NULL.
  * @param cellDrawer  Blockmap cell content drawing callback. Can be @a NULL.
  */
-static void rendBlockmap(Blockmap &bmap, mobj_t *followMobj,
-    int (*cellDrawer) (Blockmap &bmap, Blockmap::Cell const &cell, void *parameters))
+static void rendBlockmap(Blockmap const &bmap, mobj_t *followMobj,
+    int (*cellDrawer) (Blockmap const &bmap, Blockmap::Cell const &cell, void *parameters))
 {
     Blockmap::CellBlock vCellBlock;
     Blockmap::Cell vCell;
@@ -511,10 +511,10 @@ static void rendBlockmap(Blockmap &bmap, mobj_t *followMobj,
 
 void Rend_BlockmapDebug()
 {
-    int (*cellDrawer) (Blockmap &blockmap, Blockmap::Cell const &cell, void *parameters);
+    int (*cellDrawer) (Blockmap const &blockmap, Blockmap::Cell const &cell, void *parameters);
     char const *objectTypeName;
     mobj_t *followMobj = 0;
-    Blockmap *blockmap;
+    Blockmap const *blockmap;
     Point2Raw origin;
     float scale;
 
diff --git a/doomsday/client/src/world/blockmap.cpp b/doomsday/client/src/world/blockmap.cpp
index 90d45a3fb9..560fd4de35 100644
--- a/doomsday/client/src/world/blockmap.cpp
+++ b/doomsday/client/src/world/blockmap.cpp
@@ -320,7 +320,8 @@ int Blockmap::cellElementCount(Cell const &cell) const
     return 0;
 }
 
-int Blockmap::iterate(Cell const &cell, int (*callback) (void *elem, void *parameters), void *parameters)
+int Blockmap::iterate(Cell const &cell, int (*callback) (void *elem, void *parameters),
+                      void *parameters) const
 {
     if(!callback) return false; // Huh?
     if(CellData *cellData = (CellData *)d->cellData(cell))
@@ -343,7 +344,8 @@ static int cellDataIterateWorker(void *cdPtr, void *parameters)
     return cellData->iterate(p->callback, p->parameters);
 }
 
-int Blockmap::iterate(CellBlock const &cellBlock, int (*callback) (void *elem, void *parameters), void *parameters)
+int Blockmap::iterate(CellBlock const &cellBlock, int (*callback) (void *elem, void *parameters),
+                      void *parameters) const
 {
     if(!callback) return false; // Huh?
     CellDataIterateWorkerParams parm;
diff --git a/doomsday/client/src/world/map.cpp b/doomsday/client/src/world/map.cpp
index 5017ef76bd..e0d523f6c3 100644
--- a/doomsday/client/src/world/map.cpp
+++ b/doomsday/client/src/world/map.cpp
@@ -1206,22 +1206,22 @@ void Map::initNodePiles()
     LOG_INFO(String("Completed in %1 seconds.").arg(begunAt.since(), 0, 'g', 2));
 }
 
-Blockmap *Map::mobjBlockmap() const
+Blockmap const *Map::mobjBlockmap() const
 {
     return d->mobjBlockmap.data();
 }
 
-Blockmap *Map::polyobjBlockmap() const
+Blockmap const *Map::polyobjBlockmap() const
 {
     return d->polyobjBlockmap.data();
 }
 
-Blockmap *Map::lineBlockmap() const
+Blockmap const *Map::lineBlockmap() const
 {
     return d->lineBlockmap.data();
 }
 
-Blockmap *Map::bspLeafBlockmap() const
+Blockmap const *Map::bspLeafBlockmap() const
 {
     return d->bspLeafBlockmap.data();
 }