diff --git a/binaries/data/mods/public/maps/random/lorraine_plain.js b/binaries/data/mods/public/maps/random/lorraine_plain.js
index f6c1b27d90..26a8449765 100644
--- a/binaries/data/mods/public/maps/random/lorraine_plain.js
+++ b/binaries/data/mods/public/maps/random/lorraine_plain.js
@@ -129,7 +129,7 @@ for (let i = 0; i <= randIntInclusive(3, scaleByMapSize(4, 6)); ++i)
 		"smoothWidth": 2,
 		"startHeight": heightShallows,
 		"endHeight": heightShallows,
-		"maxHeight": heightShallows,
+		"constraint": new HeightConstraint(-Infinity, heightShallows),
 		"tileClass": clShallow
 	});
 }
diff --git a/binaries/data/mods/public/maps/random/ratumacos.js b/binaries/data/mods/public/maps/random/ratumacos.js
index 46d74c4fe1..8faafa3257 100644
--- a/binaries/data/mods/public/maps/random/ratumacos.js
+++ b/binaries/data/mods/public/maps/random/ratumacos.js
@@ -86,8 +86,7 @@ for (let i = 0; i < scaleByMapSize(5, 12); ++i)
 		"smoothWidth": 2,
 		"startHeight": heightShallow,
 		"endHeight": heightShallow,
-		"maxHeight": heightShallow,
-		"terrain": "blue"
+		"constraint": new HeightConstraint(-Infinity, heightShallow)
 	});
 }
 
diff --git a/binaries/data/mods/public/maps/random/rmgen-common/gaia_terrain.js b/binaries/data/mods/public/maps/random/rmgen-common/gaia_terrain.js
index 57e2da867c..23e2c47b67 100644
--- a/binaries/data/mods/public/maps/random/rmgen-common/gaia_terrain.js
+++ b/binaries/data/mods/public/maps/random/rmgen-common/gaia_terrain.js
@@ -509,9 +509,9 @@ function createTributaryRivers(riverAngle, riverCount, riverWidth, heightRiverbe
 				"startWidth": scaleByMapSize(8, 12),
 				"endWidth": scaleByMapSize(8, 12),
 				"smoothWidth": 2,
+				"constraint": new HeightConstraint(-Infinity, heightShallow),
 				"startHeight": heightShallow,
 				"endHeight": heightShallow,
-				"maxHeight": heightShallow,
 				"tileClass": shallowTileClass
 			});
 	}
@@ -523,6 +523,7 @@ function createTributaryRivers(riverAngle, riverCount, riverWidth, heightRiverbe
  *
  * @property {Vector2D} start - Location of the passage.
  * @property {Vector2D} end
+ * @property {Constraint} [constraint] - Only tiles that meet this constraint are changed.
  * @property {number} startWidth - Size of the passage (perpendicular to the direction of the passage).
  * @property {number} endWidth
  * @property {number} [startHeight] - Fixed height to be used if the height at the location shouldn't be used.
@@ -557,7 +558,7 @@ function createPassage(args)
 			let location = Vector2D.add(locationLength, Vector2D.mult(widthDirection, stepWidth)).round();
 
 			if (!g_Map.inMapBounds(location) ||
-			    args.maxHeight !== undefined && g_Map.getHeight(location) > args.maxHeight)
+			    args.constraint && !args.constraint.allows(location))
 				continue;
 
 			points.push(location);
diff --git a/binaries/data/mods/public/maps/random/sahel_watering_holes.js b/binaries/data/mods/public/maps/random/sahel_watering_holes.js
index 05d2324686..0722fc3c0d 100644
--- a/binaries/data/mods/public/maps/random/sahel_watering_holes.js
+++ b/binaries/data/mods/public/maps/random/sahel_watering_holes.js
@@ -135,7 +135,7 @@ for (let i = 0; i < numPlayers; ++i)
 		"smoothWidth": 4,
 		"startHeight": heightShallows,
 		"endHeight": heightShallows,
-		"maxHeight": heightShallows,
+		"constraint": new HeightConstraint(-Infinity, heightShallows),
 		"tileClass": clShallows
 	});
 
diff --git a/binaries/data/mods/public/maps/random/snowflake_searocks.js b/binaries/data/mods/public/maps/random/snowflake_searocks.js
index 0730f14647..8d7a160170 100644
--- a/binaries/data/mods/public/maps/random/snowflake_searocks.js
+++ b/binaries/data/mods/public/maps/random/snowflake_searocks.js
@@ -263,7 +263,7 @@ for (let i = 0; i < numIslands; ++i)
 				"startWidth": 11,
 				"endWidth": 11,
 				"smoothWidth": 3,
-				"maxHeight": heightIsland - 1,
+				"constraint": new HeightConstraint(-Infinity, heightIsland - 1),
 				"tileClass": clLand,
 				"terrain": tHill,
 				"edgeTerrain": tCliff