diff --git a/src/k_follower.c b/src/k_follower.c
index f288d63f1..78e233e4c 100644
--- a/src/k_follower.c
+++ b/src/k_follower.c
@@ -419,6 +419,7 @@ void K_HandleFollower(player_t *player)
 		K_UpdateFollowerState(player->follower, fl->idlestate, FOLLOWERSTATE_IDLE);
 
 		P_SetTarget(&player->follower->target, player->mo); // we need that to know when we need to disappear
+		P_SetTarget(&player->follower->punt_ref, player->mo);
 		player->follower->angle = player->follower->old_angle = player->mo->angle;
 
 		// This is safe to only spawn it here, the follower is removed then respawned when switched.
@@ -427,10 +428,12 @@ void K_HandleFollower(player_t *player)
 			bmobj = P_SpawnMobj(player->follower->x, player->follower->y, player->follower->z, MT_FOLLOWERBUBBLE_FRONT);
 			P_SetTarget(&player->follower->hnext, bmobj);
 			P_SetTarget(&bmobj->target, player->follower); // Used to know if we have to despawn at some point.
+			P_SetTarget(&bmobj->punt_ref, player->mo);
 
 			bmobj = P_SpawnMobj(player->follower->x, player->follower->y, player->follower->z, MT_FOLLOWERBUBBLE_BACK);
 			P_SetTarget(&player->follower->hnext->hnext, bmobj); // this seems absolutely stupid, I know, but this will make updating the momentums/flags of these a bit easier.
 			P_SetTarget(&bmobj->target, player->follower); // Ditto
+			P_SetTarget(&bmobj->punt_ref, player->mo);
 		}
 	}
 	else // follower exists, woo!
diff --git a/src/k_kart.c b/src/k_kart.c
index 46972f9a0..6f57ffe2b 100644
--- a/src/k_kart.c
+++ b/src/k_kart.c
@@ -8082,6 +8082,9 @@ static void K_UpdateTripwire(player_t *player)
 			P_SetTarget(&front->target, player->mo);
 			P_SetTarget(&back->target, player->mo);
 
+			P_SetTarget(&front->punt_ref, player->mo);
+			P_SetTarget(&back->punt_ref, player->mo);
+
 			front->dispoffset = 1;
 			front->old_angle = back->old_angle = K_MomentumAngle(player->mo);
 			back->dispoffset = -1;
diff --git a/src/objects/emerald.c b/src/objects/emerald.c
index 65b23edb6..e749efb92 100644
--- a/src/objects/emerald.c
+++ b/src/objects/emerald.c
@@ -276,6 +276,7 @@ static void spawn_lens_flare(mobj_t *emerald)
 void Obj_BeginEmeraldOrbit(mobj_t *emerald, mobj_t *target, fixed_t radius, INT32 revolution_time, tic_t fuse)
 {
 	P_SetTarget(&emerald_orbit(emerald), target);
+	P_SetTarget(&emerald->punt_ref, target);
 
 	if (P_MobjWasRemoved(emerald_award(emerald)))
 	{
diff --git a/src/p_mobj.c b/src/p_mobj.c
index 11f804ab8..f5b14929c 100644
--- a/src/p_mobj.c
+++ b/src/p_mobj.c
@@ -5434,6 +5434,9 @@ void P_RunOverlays(void)
 		mo->scale = mo->destscale = FixedMul(mo->target->scale, mo->movefactor);
 		mo->angle = (mo->target->player ? mo->target->player->drawangle : mo->target->angle) + mo->movedir;
 
+		P_SetTarget(&mo->punt_ref, mo->target->punt_ref);
+		mo->reappear = mo->target->reappear;
+
 		if (!(mo->threshold & OV_DONTSCREENOFFSET))
 		{
 			mo->spritexoffset = mo->target->spritexoffset;
diff --git a/src/p_user.c b/src/p_user.c
index b1a0fd3cd..d5e781e19 100644
--- a/src/p_user.c
+++ b/src/p_user.c
@@ -1332,6 +1332,11 @@ void P_DoPlayerExit(player_t *player, pflags_t flags)
 		{
 			G_BeginLevelExit();
 		}
+
+		if (specialstageinfo.valid == true && losing == false && P_MobjWasRemoved(player->mo) == false)
+		{
+			K_MakeObjectReappear(player->mo);
+		}
 	}
 
 	K_InitPlayerTally(player);