diff --git a/src/saveload/afterload.cpp b/src/saveload/afterload.cpp
--- a/src/saveload/afterload.cpp
+++ b/src/saveload/afterload.cpp
@@ -528,6 +528,25 @@ static uint FixVehicleInclination(Vehicl
 }
 
 /**
+ * Check whether the ground vehicles are at the correct Z-coordinate. When they
+ * are not, this will cause all kinds of problems later on as the vehicle might
+ * not get onto bridges and so on.
+ */
+static void CheckGroundVehiclesAtCorrectZ()
+{
+	for (Vehicle *v : Vehicle::Iterate()) {
+		if (v->IsGroundVehicle()) {
+			/*
+			 * Either the vehicle is not actually on the given tile, i.e. it is
+			 * in the wormhole of a bridge or a tunnel, or the Z-coordinate must
+			 * be the same as when it would be recalculated right now.
+			 */
+			assert(v->tile != TileVirtXY(v->x_pos, v->y_pos) || v->z_pos == GetSlopePixelZ(v->x_pos, v->y_pos, true));
+		}
+	}
+}
+
+/**
  * Checks for the possibility that a bridge may be on this tile
  * These are in fact all the tile types on which a bridge can be found
  * @param t The tile to analyze
@@ -1249,7 +1268,7 @@ bool AfterLoadGame()
 					case DIAGDIR_SW: if ((v->x_pos & 0xF) != TILE_SIZE - 1) continue; break;
 					case DIAGDIR_NW: if ((v->y_pos & 0xF) !=  0)            continue; break;
 				}
-			} else if (v->z_pos > GetSlopePixelZ(v->x_pos, v->y_pos, true)) {
+			} else if (v->z_pos > GetTileMaxPixelZ(TileVirtXY(v->x_pos, v->y_pos))) {
 				v->tile = GetNorthernBridgeEnd(v->tile);
 				v->UpdatePosition();
 			} else {
@@ -2594,6 +2613,24 @@ bool AfterLoadGame()
 		}
 	}
 
+
+	if (IsSavegameVersionBefore(SLV_CONSISTENT_PARTIAL_Z)) {
+		/*
+		 * The logic of GetPartialPixelZ has been changed, so the resulting Zs on
+		 * the map are consistent. This requires that the Z position of some
+		 * vehicles is updated to reflect this new situation.
+		 *
+		 * This needs to be before SLV_158, because that performs asserts using
+		 * GetSlopePixelZ which internally uses GetPartialPixelZ.
+		 */
+		for (Vehicle *v : Vehicle::Iterate()) {
+			if (v->IsGroundVehicle() && TileVirtXY(v->x_pos, v->y_pos) == v->tile) {
+				/* Vehicle is on the ground, and not in a wormhole. */
+				v->z_pos = GetSlopePixelZ(v->x_pos, v->y_pos, true);
+			}
+		}
+	}
+
 	if (IsSavegameVersionBefore(SLV_158)) {
 		for (Vehicle *v : Vehicle::Iterate()) {
 			switch (v->type) {
@@ -3228,6 +3265,8 @@ bool AfterLoadGame()
 
 	AfterLoadLinkGraphs();
 
+	CheckGroundVehiclesAtCorrectZ();
+
 	/* Start the scripts. This MUST happen after everything else except
 	 * starting a new company. */
 	StartScripts();