diff --git a/src/gfx/process.cpp b/src/gfx/process.cpp
index 29b94565..17b7c66f 100644
--- a/src/gfx/process.cpp
+++ b/src/gfx/process.cpp
@@ -695,12 +695,6 @@ static void outputUnoptimizedMaps(
 	uint8_t tileID = 0;
 	uint8_t bank = 0;
 	for (AttrmapEntry const &attr : attrmap) {
-		if (tileID == options.maxNbTiles[bank]) {
-			assume(bank == 0);
-			bank = 1;
-			tileID = 0;
-		}
-
 		if (tilemapOutput.has_value()) {
 			(*tilemapOutput)
 			    ->sputc((attr.isBackgroundTile() ? 0 : tileID) + options.baseTileIDs[bank]);
@@ -714,8 +708,17 @@ static void outputUnoptimizedMaps(
 		}
 
 		// Background tiles are skipped in the tile data, so they should be skipped in the maps too.
-		if (!attr.isBackgroundTile()) {
+		if (attr.isBackgroundTile()) {
+			continue;
+		}
+
+		// Compare with `maxNbTiles` *before* incrementing, due to unsigned overflow!
+		if (tileID + 1 < options.maxNbTiles[bank]) {
 			++tileID;
+		} else {
+			assume(bank == 0);
+			bank = 1;
+			tileID = 0;
 		}
 	}
 }
diff --git a/test/gfx/unoptimized-full.2bpp b/test/gfx/unoptimized-full.2bpp
new file mode 100644
index 00000000..8e1d54fe
Binary files /dev/null and b/test/gfx/unoptimized-full.2bpp differ
diff --git a/test/gfx/unoptimized-full.attrmap b/test/gfx/unoptimized-full.attrmap
new file mode 100644
index 00000000..fe8b860f
Binary files /dev/null and b/test/gfx/unoptimized-full.attrmap differ
diff --git a/test/gfx/unoptimized-full.flags b/test/gfx/unoptimized-full.flags
new file mode 100644
index 00000000..9dcb6275
--- /dev/null
+++ b/test/gfx/unoptimized-full.flags
@@ -0,0 +1 @@
+-N 256,256
diff --git a/test/gfx/unoptimized-full.pal b/test/gfx/unoptimized-full.pal
new file mode 100644
index 00000000..aa90be83
Binary files /dev/null and b/test/gfx/unoptimized-full.pal differ
diff --git a/test/gfx/unoptimized-full.png b/test/gfx/unoptimized-full.png
new file mode 100644
index 00000000..cd48d42f
Binary files /dev/null and b/test/gfx/unoptimized-full.png differ
diff --git a/test/gfx/unoptimized-full.tilemap b/test/gfx/unoptimized-full.tilemap
new file mode 100644
index 00000000..553a99f9
Binary files /dev/null and b/test/gfx/unoptimized-full.tilemap differ