diff --git a/src/landscape.cpp b/src/landscape.cpp
index b94e315b95..00640f9486 100644
--- a/src/landscape.cpp
+++ b/src/landscape.cpp
@@ -723,11 +723,11 @@ void RunTileLoop()
 	 * shift register (LFSR). This allows a deterministic pseudorandom ordering, but
 	 * still with minimal state and fast iteration. */
 
-	/* Maximal length LFSR feedback terms, from 12-bit (for 64x64 maps) to 26-bit (for 8kx8k maps).
+	/* Maximal length LFSR feedback terms, from 12-bit (for 64x64 maps) to 28-bit (for 16kx16k maps).
 	 * Extracted from http://www.ece.cmu.edu/~koopman/lfsr/ */
 	static const uint32 feedbacks[] = {
 		0xD8F, 0x1296, 0x2496, 0x4357, 0x8679, 0x1030E, 0x206CD, 0x403FE, 0x807B8, 0x1004B2, 0x2006A8,
-		0x4004B2, 0x800B87, 0x10004F3, 0x200072D,
+		0x4004B2, 0x800B87, 0x10004F3, 0x200072D, 0x40006AE, 0x80009E3,
 	};
 	assert_compile(lengthof(feedbacks) == MAX_MAP_TILES_BITS - 2 * MIN_MAP_SIZE_BITS + 1);
 	const uint32 feedback = feedbacks[MapLogX() + MapLogY() - 2 * MIN_MAP_SIZE_BITS];
diff --git a/src/map_type.h b/src/map_type.h
index 7e50a03140..d2403fdb3d 100644
--- a/src/map_type.h
+++ b/src/map_type.h
@@ -63,10 +63,10 @@ struct TileIndexDiffC {
 /** Minimal and maximal map width and height */
 static const uint MIN_MAP_SIZE_BITS = 6;                      ///< Minimal size of map is equal to 2 ^ MIN_MAP_SIZE_BITS
 static const uint MAX_MAP_SIZE_BITS = 20;                     ///< Maximal size of map is equal to 2 ^ MAX_MAP_SIZE_BITS
-static const uint MAX_MAP_TILES_BITS = 26;                    ///< Maximal number of tiles in a map is equal to 2 ^ MAX_MAP_TILES_BITS.
+static const uint MAX_MAP_TILES_BITS = 28;                    ///< Maximal number of tiles in a map is equal to 2 ^ MAX_MAP_TILES_BITS.
 static const uint MIN_MAP_SIZE      = 1 << MIN_MAP_SIZE_BITS; ///< Minimal map size = 64
 static const uint MAX_MAP_SIZE      = 1 << MAX_MAP_SIZE_BITS; ///< Maximal map size = 1M
-static const uint MAX_MAP_TILES     = 1 << MAX_MAP_TILES_BITS;///< Maximal number of tiles in a map = 64M
+static const uint MAX_MAP_TILES     = 1 << MAX_MAP_TILES_BITS;///< Maximal number of tiles in a map = 256M (16k x 16k)
 
 /**
  * Approximation of the length of a straight track, relative to a diagonal
diff --git a/src/newgrf_debug_gui.cpp b/src/newgrf_debug_gui.cpp
index 2ec678aea7..af9094c693 100644
--- a/src/newgrf_debug_gui.cpp
+++ b/src/newgrf_debug_gui.cpp
@@ -699,6 +699,7 @@ static WindowDesc _newgrf_inspect_desc(
  */
 void ShowNewGRFInspectWindow(GrfSpecFeature feature, uint index, const uint32 grfid)
 {
+	if (index >= (1 << 27)) return;
 	if (!IsNewGRFInspectable(feature, index)) return;
 
 	WindowNumber wno = GetInspectWindowNumber(feature, index);
@@ -718,6 +719,7 @@ void ShowNewGRFInspectWindow(GrfSpecFeature feature, uint index, const uint32 gr
 void InvalidateNewGRFInspectWindow(GrfSpecFeature feature, uint index)
 {
 	if (feature == GSF_INVALID) return;
+	if (index >= (1 << 27)) return;
 
 	WindowNumber wno = GetInspectWindowNumber(feature, index);
 	InvalidateWindowData(WC_NEWGRF_INSPECT, wno);
@@ -734,6 +736,7 @@ void InvalidateNewGRFInspectWindow(GrfSpecFeature feature, uint index)
 void DeleteNewGRFInspectWindow(GrfSpecFeature feature, uint index)
 {
 	if (feature == GSF_INVALID) return;
+	if (index >= (1 << 27)) return;
 
 	WindowNumber wno = GetInspectWindowNumber(feature, index);
 	DeleteWindowById(WC_NEWGRF_INSPECT, wno);
@@ -755,6 +758,7 @@ void DeleteNewGRFInspectWindow(GrfSpecFeature feature, uint index)
  */
 bool IsNewGRFInspectable(GrfSpecFeature feature, uint index)
 {
+	if (index >= (1 << 27)) return false;
 	const NIFeature *nif = GetFeature(GetInspectWindowNumber(feature, index));
 	if (nif == NULL) return false;
 	return nif->helper->IsInspectable(index);