diff --git a/src/p_teleport.cpp b/src/p_teleport.cpp
index 6ba60be0eb..59359a981b 100644
--- a/src/p_teleport.cpp
+++ b/src/p_teleport.cpp
@@ -35,6 +35,8 @@
 #include "i_system.h"
 #include "doomstat.h"
 
+#define FUDGEFACTOR		10
+
 static FRandom pr_teleport ("Teleport");
 
 extern void P_CalcHeight (player_t *player);
@@ -476,16 +478,52 @@ bool EV_SilentLineTeleport (line_t *line, int side, AActor *thing, int id, INTBO
 			player_t *player = thing->player && thing->player->mo == thing ?
 				thing->player : NULL;
 
-			// Height of thing above ground
-			fixed_t z;
-			
-			z = thing->z - line->backsector->floorplane.ZatPoint (thing->x, thing->y)
-				+ l->frontsector->floorplane.ZatPoint (x, y);
+			// Whether walking towards first side of exit linedef steps down
+			bool stepdown = l->frontsector->floorplane.ZatPoint(x, y) < l->backsector->floorplane.ZatPoint(x, y);
+
+			// Height of thing above ground
+			fixed_t z = thing->z - thing->floorz;
+
+			// Side to exit the linedef on positionally.
+			//
+			// Notes:
+			//
+			// This flag concerns exit position, not momentum. Due to
+			// roundoff error, the thing can land on either the left or
+			// the right side of the exit linedef, and steps must be
+			// taken to make sure it does not end up on the wrong side.
+			//
+			// Exit momentum is always towards side 1 in a reversed
+			// teleporter, and always towards side 0 otherwise.
+			//
+			// Exiting positionally on side 1 is always safe, as far
+			// as avoiding oscillations and stuck-in-wall problems,
+			// but may not be optimum for non-reversed teleporters.
+			//
+			// Exiting on side 0 can cause oscillations if momentum
+			// is towards side 1, as it is with reversed teleporters.
+			//
+			// Exiting on side 1 slightly improves player viewing
+			// when going down a step on a non-reversed teleporter.
+
+			int side = reverse || (player && stepdown);
+			int fudge = FUDGEFACTOR;
+
+			// Make sure we are on correct side of exit linedef.
+			while (P_PointOnLineSide(x, y, l) != side && --fudge >= 0)
+			{
+				if (abs(l->dx) > abs(l->dy))
+					y -= l->dx < 0 != side ? -1 : 1;
+				else
+					x += l->dy < 0 != side ? -1 : 1;
+			}
 
-			// Attempt to teleport, aborting if blocked
 			// Adjust z position to be same height above ground as before.
 			// Ground level at the exit is measured as the higher of the
 			// two floor heights at the exit linedef.
+			z = z + l->sidedef[stepdown]->sector->floorplane.ZatPoint(x, y);
+
+			// Attempt to teleport, aborting if blocked
 			if (!P_TeleportMove (thing, x, y, z, false))
 			{
 				return false;