diff --git a/src/landscape.cpp b/src/landscape.cpp
index 79b24baf72..991a445ad8 100644
--- a/src/landscape.cpp
+++ b/src/landscape.cpp
@@ -131,9 +131,15 @@ Point InverseRemapCoords2(int x, int y, bool clamp_to_map, bool *clamped)
 	 * (FOUNDATION_HALFTILE_LOWER on SLOPE_STEEP_S hides north halftile completely)
 	 * So give it a z-malus of 4 in the first iterations. */
 	int z = 0;
-	for (int i = 0; i < 5; i++) z = GetSlopePixelZ(Clamp(pt.x + max(z, 4) - 4, min_coord, max_x), Clamp(pt.y + max(z, 4) - 4, min_coord, max_y)) / 2;
-	for (int m = 3; m > 0; m--) z = GetSlopePixelZ(Clamp(pt.x + max(z, m) - m, min_coord, max_x), Clamp(pt.y + max(z, m) - m, min_coord, max_y)) / 2;
-	for (int i = 0; i < 5; i++) z = GetSlopePixelZ(Clamp(pt.x + z,             min_coord, max_x), Clamp(pt.y + z,             min_coord, max_y)) / 2;
+	if (clamp_to_map) {
+		for (int i = 0; i < 5; i++) z = GetSlopePixelZ(Clamp(pt.x + max(z, 4) - 4, min_coord, max_x), Clamp(pt.y + max(z, 4) - 4, min_coord, max_y)) / 2;
+		for (int m = 3; m > 0; m--) z = GetSlopePixelZ(Clamp(pt.x + max(z, m) - m, min_coord, max_x), Clamp(pt.y + max(z, m) - m, min_coord, max_y)) / 2;
+		for (int i = 0; i < 5; i++) z = GetSlopePixelZ(Clamp(pt.x + z,             min_coord, max_x), Clamp(pt.y + z,             min_coord, max_y)) / 2;
+	} else {
+		for (int i = 0; i < 5; i++) z = GetSlopePixelZOutsideMap(pt.x + max(z, 4) - 4, pt.y + max(z, 4) - 4) / 2;
+		for (int m = 3; m > 0; m--) z = GetSlopePixelZOutsideMap(pt.x + max(z, m) - m, pt.y + max(z, m) - m) / 2;
+		for (int i = 0; i < 5; i++) z = GetSlopePixelZOutsideMap(pt.x + z,             pt.y + z            ) / 2;
+	}
 
 	pt.x += z;
 	pt.y += z;
@@ -342,6 +348,23 @@ int GetSlopePixelZ(int x, int y)
 	return _tile_type_procs[GetTileType(tile)]->get_slope_z_proc(tile, x, y);
 }
 
+/**
+ * Return world \c z coordinate of a given point of a tile,
+ * also for tiles outside the map (virtual "black" tiles).
+ *
+ * @param x World X coordinate in tile "units", may be ouside the map.
+ * @param y World Y coordinate in tile "units", may be ouside the map.
+ * @return World Z coordinate at tile ground level, including slopes and foundations.
+ */
+int GetSlopePixelZOutsideMap(int x, int y)
+{
+	if (IsInsideBS(x, 0, MapSizeX() * TILE_SIZE) && IsInsideBS(y, 0, MapSizeY() * TILE_SIZE)) {
+		return GetSlopePixelZ(x, y);
+	} else {
+		return _tile_type_procs[MP_VOID]->get_slope_z_proc(INVALID_TILE, x, y);
+	}
+}
+
 /**
  * Determine the Z height of a corner relative to TileZ.
  *
diff --git a/src/landscape.h b/src/landscape.h
index d24d0d190d..43d9e5f2e6 100644
--- a/src/landscape.h
+++ b/src/landscape.h
@@ -40,6 +40,7 @@ Slope GetFoundationSlope(TileIndex tile, int *z = NULL);
 
 uint GetPartialPixelZ(int x, int y, Slope corners);
 int GetSlopePixelZ(int x, int y);
+int GetSlopePixelZOutsideMap(int x, int y);
 void GetSlopePixelZOnEdge(Slope tileh, DiagDirection edge, int *z1, int *z2);
 
 /**
diff --git a/src/tile_map.cpp b/src/tile_map.cpp
index 05b0ea1942..200a203089 100644
--- a/src/tile_map.cpp
+++ b/src/tile_map.cpp
@@ -14,60 +14,6 @@
 
 #include "safeguards.h"
 
-/**
- * Returns the tile height for a coordinate outside map.  Such a height is
- * needed for painting the area outside map using completely black tiles.
- * The idea is descending to heightlevel 0 as fast as possible.
- * @param x The X-coordinate (same unit as TileX).
- * @param y The Y-coordinate (same unit as TileY).
- * @return The height in the same unit as TileHeight.
- */
-uint TileHeightOutsideMap(int x, int y)
-{
-	/* In all cases: Descend to heightlevel 0 as fast as possible.
-	 * So: If we are at the 0-side of the map (x<0 or y<0), we must
-	 * subtract the distance to coordinate 0 from the heightlevel at
-	 * coordinate 0.
-	 * In other words: Subtract e.g. -x. If we are at the MapMax
-	 * side of the map, we also need to subtract the distance to
-	 * the edge of map, e.g. MapMaxX - x.
-	 *
-	 * NOTE: Assuming constant heightlevel outside map would be
-	 * simpler here. However, then we run into painting problems,
-	 * since whenever a heightlevel change at the map border occurs,
-	 * we would need to repaint anything outside map.
-	 * In contrast, by doing it this way, we can localize this change,
-	 * which means we may assume constant heightlevel for all tiles
-	 * at more than <heightlevel at map border> distance from the
-	 * map border.
-	 */
-	if (x < 0) {
-		if (y < 0) {
-			return max((int)TileHeight(TileXY(0, 0)) - (-x) - (-y), 0);
-		} else if (y < (int)MapMaxY()) {
-			return max((int)TileHeight(TileXY(0, y)) - (-x), 0);
-		} else {
-			return max((int)TileHeight(TileXY(0, (int)MapMaxY())) - (-x) - (y - (int)MapMaxY()), 0);
-		}
-	} else if (x < (int)MapMaxX()) {
-		if (y < 0) {
-			return max((int)TileHeight(TileXY(x, 0)) - (-y), 0);
-		} else if (y < (int)MapMaxY()) {
-			return TileHeight(TileXY(x, y));
-		} else {
-			return max((int)TileHeight(TileXY(x, (int)MapMaxY())) - (y - (int)MapMaxY()), 0);
-		}
-	} else {
-		if (y < 0) {
-			return max((int)TileHeight(TileXY((int)MapMaxX(), 0)) - (x - (int)MapMaxX()) - (-y), 0);
-		} else if (y < (int)MapMaxY()) {
-			return max((int)TileHeight(TileXY((int)MapMaxX(), y)) - (x - (int)MapMaxX()), 0);
-		} else {
-			return max((int)TileHeight(TileXY((int)MapMaxX(), (int)MapMaxY())) - (x - (int)MapMaxX()) - (y - (int)MapMaxY()), 0);
-		}
-	}
-}
-
 /**
  * Get a tile's slope given the heigh of its four corners.
  * @param hnorth The height at the northern corner in the same unit as TileHeight.
@@ -114,30 +60,26 @@ static Slope GetTileSlopeGivenHeight(int hnorth, int hwest, int heast, int hsout
  */
 Slope GetTileSlope(TileIndex tile, int *h)
 {
-	assert(tile < MapSize());
+	uint x1 = TileX(tile);
+	uint y1 = TileY(tile);
+	uint x2 = min(x1 + 1, MapMaxX());
+	uint y2 = min(y1 + 1, MapMaxY());
 
-	uint x = TileX(tile);
-	uint y = TileY(tile);
-	if (x == MapMaxX() || y == MapMaxY()) {
-		if (h != NULL) *h = TileHeight(tile);
-		return SLOPE_FLAT;
-	}
-
-	int hnorth = TileHeight(tile);                    // Height of the North corner.
-	int hwest  = TileHeight(tile + TileDiffXY(1, 0)); // Height of the West corner.
-	int heast  = TileHeight(tile + TileDiffXY(0, 1)); // Height of the East corner.
-	int hsouth = TileHeight(tile + TileDiffXY(1, 1)); // Height of the South corner.
+	int hnorth = TileHeight(tile);           // Height of the North corner.
+	int hwest  = TileHeight(TileXY(x2, y1)); // Height of the West corner.
+	int heast  = TileHeight(TileXY(x1, y2)); // Height of the East corner.
+	int hsouth = TileHeight(TileXY(x2, y2)); // Height of the South corner.
 
 	return GetTileSlopeGivenHeight(hnorth, hwest, heast, hsouth, h);
 }
 
 /**
- * Return the slope of a given tile outside the map.
+ * Return the slope of a given tile, also for tiles outside the map (virtual "black" tiles).
  *
- * @param x X-coordinate of the tile outside to compute height of.
- * @param y Y-coordinate of the tile outside to compute height of.
- * @param h    If not \c NULL, pointer to storage of z height.
- * @return Slope of the tile outside map, except for the HALFTILE part.
+ * @param x X coordinate of the tile to compute slope of, may be ouside the map.
+ * @param y Y coordinate of the tile to compute slope of, may be ouside the map.
+ * @param h If not \c NULL, pointer to storage of z height.
+ * @return Slope of the tile, except for the HALFTILE part.
  */
 Slope GetTilePixelSlopeOutsideMap(int x, int y, int *h)
 {
@@ -159,17 +101,15 @@ Slope GetTilePixelSlopeOutsideMap(int x, int y, int *h)
  */
 bool IsTileFlat(TileIndex tile, int *h)
 {
-	assert(tile < MapSize());
-
-	if (!IsInnerTile(tile)) {
-		if (h != NULL) *h = TileHeight(tile);
-		return true;
-	}
+	uint x1 = TileX(tile);
+	uint y1 = TileY(tile);
+	uint x2 = min(x1 + 1, MapMaxX());
+	uint y2 = min(y1 + 1, MapMaxY());
 
 	uint z = TileHeight(tile);
-	if (TileHeight(tile + TileDiffXY(1, 0)) != z) return false;
-	if (TileHeight(tile + TileDiffXY(0, 1)) != z) return false;
-	if (TileHeight(tile + TileDiffXY(1, 1)) != z) return false;
+	if (TileHeight(TileXY(x2, y1)) != z) return false;
+	if (TileHeight(TileXY(x1, y2)) != z) return false;
+	if (TileHeight(TileXY(x2, y2)) != z) return false;
 
 	if (h != NULL) *h = z;
 	return true;
@@ -182,12 +122,15 @@ bool IsTileFlat(TileIndex tile, int *h)
  */
 int GetTileZ(TileIndex tile)
 {
-	if (TileX(tile) == MapMaxX() || TileY(tile) == MapMaxY()) return 0;
+	uint x1 = TileX(tile);
+	uint y1 = TileY(tile);
+	uint x2 = min(x1 + 1, MapMaxX());
+	uint y2 = min(y1 + 1, MapMaxY());
 
-	int h =    TileHeight(tile);                     // N corner
-	h = min(h, TileHeight(tile + TileDiffXY(1, 0))); // W corner
-	h = min(h, TileHeight(tile + TileDiffXY(0, 1))); // E corner
-	h = min(h, TileHeight(tile + TileDiffXY(1, 1))); // S corner
+	int h =    TileHeight(tile);            // N corner
+	h = min(h, TileHeight(TileXY(x2, y1))); // W corner
+	h = min(h, TileHeight(TileXY(x1, y2))); // E corner
+	h = min(h, TileHeight(TileXY(x2, y2))); // S corner
 
 	return h;
 }
@@ -199,12 +142,15 @@ int GetTileZ(TileIndex tile)
  */
 int GetTileMaxZ(TileIndex t)
 {
-	if (TileX(t) == MapMaxX() || TileY(t) == MapMaxY()) return TileHeightOutsideMap(TileX(t), TileY(t));
+	uint x1 = TileX(t);
+	uint y1 = TileY(t);
+	uint x2 = min(x1 + 1, MapMaxX());
+	uint y2 = min(y1 + 1, MapMaxY());
 
-	int h =         TileHeight(t);                     // N corner
-	h = max<int>(h, TileHeight(t + TileDiffXY(1, 0))); // W corner
-	h = max<int>(h, TileHeight(t + TileDiffXY(0, 1))); // E corner
-	h = max<int>(h, TileHeight(t + TileDiffXY(1, 1))); // S corner
+	int h =         TileHeight(t);               // N corner
+	h = max<int>(h, TileHeight(TileXY(x2, y1))); // W corner
+	h = max<int>(h, TileHeight(TileXY(x1, y2))); // E corner
+	h = max<int>(h, TileHeight(TileXY(x2, y2))); // S corner
 
 	return h;
 }
diff --git a/src/tile_map.h b/src/tile_map.h
index 3fad368cd7..7a76f2b974 100644
--- a/src/tile_map.h
+++ b/src/tile_map.h
@@ -34,7 +34,17 @@ static inline uint TileHeight(TileIndex tile)
 	return _m[tile].height;
 }
 
-uint TileHeightOutsideMap(int x, int y);
+/**
+ * Returns the height of a tile, also for tiles outside the map (virtual "black" tiles).
+ *
+ * @param x X coordinate of the tile, may be ouside the map.
+ * @param y Y coordinate of the tile, may be ouside the map.
+ * @return The height in the same unit as TileHeight.
+ */
+static inline uint TileHeightOutsideMap(int x, int y)
+{
+	return TileHeight(TileXY(Clamp(x, 0, MapMaxX()), Clamp(y, 0, MapMaxY())));
+}
 
 /**
  * Sets the height of a tile.
@@ -67,11 +77,10 @@ static inline uint TilePixelHeight(TileIndex tile)
 }
 
 /**
- * Returns the tile height for a coordinate outside map.  Such a height is
- * needed for painting the area outside map using completely black tiles.
- * The idea is descending to heightlevel 0 as fast as possible.
- * @param x The X-coordinate (same unit as TileX).
- * @param y The Y-coordinate (same unit as TileY).
+ * Returns the height of a tile in pixels, also for tiles outside the map (virtual "black" tiles).
+ *
+ * @param x X coordinate of the tile, may be ouside the map.
+ * @param y Y coordinate of the tile, may be ouside the map.
  * @return The height in pixels in the same unit as TilePixelHeight.
  */
 static inline uint TilePixelHeightOutsideMap(int x, int y)
diff --git a/src/void_cmd.cpp b/src/void_cmd.cpp
index ffe54df992..a2a45e7227 100644
--- a/src/void_cmd.cpp
+++ b/src/void_cmd.cpp
@@ -10,7 +10,7 @@
 /** @file void_cmd.cpp Handling of void tiles. */
 
 #include "stdafx.h"
-#include "tile_cmd.h"
+#include "landscape.h"
 #include "command_func.h"
 #include "viewport_func.h"
 #include "slope_func.h"
@@ -28,7 +28,12 @@ static void DrawTile_Void(TileInfo *ti)
 
 static int GetSlopePixelZ_Void(TileIndex tile, uint x, uint y)
 {
-	return TilePixelHeight(tile);
+	/* This function may be called on tiles outside the map, don't asssume
+	 * that 'tile' is a valid tile index. See GetSlopePixelZOutsideMap. */
+	int z;
+	Slope tileh = GetTilePixelSlopeOutsideMap(x >> 4, y >> 4, &z);
+
+	return z + GetPartialPixelZ(x & 0xF, y & 0xF, tileh);
 }
 
 static Foundation GetFoundation_Void(TileIndex tile, Slope tileh)