diff --git a/src/common/engine/m_random.cpp b/src/common/engine/m_random.cpp
index df4d532176..ee29a80554 100644
--- a/src/common/engine/m_random.cpp
+++ b/src/common/engine/m_random.cpp
@@ -388,6 +388,21 @@ FRandom *FRandom::StaticFindRNG (const char *name, bool client)
 	return probe;
 }
 
+void FRandom::SaveRNGState(TArray<FRandom>& backups)
+{
+	for (auto cur = RNGList; cur != nullptr; cur = cur->Next)
+		backups.Push(*cur);
+}
+
+void FRandom::RestoreRNGState(TArray<FRandom>& backups)
+{
+	unsigned int i = 0u;
+	for (auto cur = RNGList; cur != nullptr; cur = cur->Next)
+		*cur = backups[i++];
+
+	backups.Clear();
+}
+
 //==========================================================================
 //
 // FRandom :: StaticPrintSeeds
diff --git a/src/g_levellocals.h b/src/g_levellocals.h
index 719427d263..c02a6bd016 100644
--- a/src/g_levellocals.h
+++ b/src/g_levellocals.h
@@ -199,7 +199,7 @@ public:
 	void ClearDynamic3DFloorData();
 	void WorldDone(void);
 	void AirControlChanged();
-	AActor *SelectTeleDest(int tid, int tag, bool norandom);
+	AActor *SelectTeleDest(int tid, int tag, bool norandom, bool isPlayer);
 	bool AlignFlat(int linenum, int side, int fc);
 	void ReplaceTextures(const char *fromname, const char *toname, int flags);
 
diff --git a/src/playsim/p_teleport.cpp b/src/playsim/p_teleport.cpp
index c39c6df1dc..be398205cc 100644
--- a/src/playsim/p_teleport.cpp
+++ b/src/playsim/p_teleport.cpp
@@ -272,7 +272,7 @@ DEFINE_ACTION_FUNCTION(AActor, Teleport)
 //
 //-----------------------------------------------------------------------------
 
-AActor *FLevelLocals::SelectTeleDest (int tid, int tag, bool norandom)
+AActor *FLevelLocals::SelectTeleDest (int tid, int tag, bool norandom, bool isPlayer)
 {
 	AActor *searcher;
 
@@ -324,7 +324,8 @@ AActor *FLevelLocals::SelectTeleDest (int tid, int tag, bool norandom)
 		{
 			if (count != 1 && !norandom)
 			{
-				count = 1 + (pr_teleport() % count);
+				// Players get their own RNG seed to reduce likelihood of breaking prediction.
+				count = 1 + ((isPlayer ? pr_playerteleport() : pr_teleport()) % count);
 			}
 			searcher = NULL;
 			while (count > 0)
@@ -395,7 +396,7 @@ bool FLevelLocals::EV_Teleport (int tid, int tag, line_t *line, int side, AActor
 	{ // Don't teleport if hit back of line, so you can get out of teleporter.
 		return 0;
 	}
-	searcher = SelectTeleDest(tid, tag, predicting);
+	searcher = SelectTeleDest(tid, tag, false, thing->player != nullptr && thing->player->mo == thing);
 	if (searcher == NULL)
 	{
 		return false;
diff --git a/src/playsim/p_user.cpp b/src/playsim/p_user.cpp
index 463d8f6e31..bdc9e9caa4 100644
--- a/src/playsim/p_user.cpp
+++ b/src/playsim/p_user.cpp
@@ -144,6 +144,8 @@ static DVector3 LastPredictedPosition;
 static int LastPredictedPortalGroup;
 static int LastPredictedTic;
 
+static TArray<FRandom> PredictionRNG;
+
 static player_t PredictionPlayerBackup;
 static AActor *PredictionActor;
 static TArray<uint8_t> PredictionActorBackupArray;
@@ -1461,6 +1463,8 @@ void P_PredictPlayer (player_t *player)
 		return;
 	}
 
+	FRandom::SaveRNGState(PredictionRNG);
+
 	// Save original values for restoration later
 	PredictionPlayerBackup.CopyFrom(*player, false);
 
@@ -1600,6 +1604,8 @@ void P_UnPredictPlayer ()
 			// Q: Can this happen? If yes, can we continue?
 		}
 
+		FRandom::RestoreRNGState(PredictionRNG);
+
 		AActor *savedcamera = player->camera;
 
 		auto &actInvSel = act->PointerVar<AActor*>(NAME_InvSel);