diff --git a/src/actor.h b/src/actor.h
index 0f9a90e0ea..ad622b3b4b 100644
--- a/src/actor.h
+++ b/src/actor.h
@@ -581,9 +581,6 @@ public:
 
 	virtual void Tick ();
 
-	// Smallest yaw interval for a mapthing to be spawned with
-	virtual angle_t AngleIncrements ();
-
 	// Called when actor dies
 	virtual void Die (AActor *source, AActor *inflictor);
 
diff --git a/src/g_shared/a_camera.cpp b/src/g_shared/a_camera.cpp
index c47c7c22d4..99da16ae72 100644
--- a/src/g_shared/a_camera.cpp
+++ b/src/g_shared/a_camera.cpp
@@ -53,7 +53,6 @@ class ASecurityCamera : public AActor
 public:
 	void PostBeginPlay ();
 	void Tick ();
-	angle_t AngleIncrements ();
 
 	void Serialize (FArchive &arc);
 protected:
@@ -71,11 +70,6 @@ void ASecurityCamera::Serialize (FArchive &arc)
 	arc << Center << Acc << Delta << Range;
 }
 
-angle_t ASecurityCamera::AngleIncrements ()
-{
-	return ANGLE_1;
-}
-
 void ASecurityCamera::PostBeginPlay ()
 {
 	Super::PostBeginPlay ();
diff --git a/src/g_shared/a_hatetarget.cpp b/src/g_shared/a_hatetarget.cpp
index 71c254bad8..3753d0bb9c 100644
--- a/src/g_shared/a_hatetarget.cpp
+++ b/src/g_shared/a_hatetarget.cpp
@@ -43,7 +43,6 @@ class AHateTarget : public AActor
 	DECLARE_CLASS (AHateTarget, AActor)
 public:
 	void BeginPlay ();
-	angle_t AngleIncrements (void);
 	int TakeSpecialDamage (AActor *inflictor, AActor *source, int damage, FName damagetype);
 };
 
@@ -77,7 +76,3 @@ int AHateTarget::TakeSpecialDamage (AActor *inflictor, AActor *source, int damag
 	}
 }
 
-angle_t AHateTarget::AngleIncrements (void)
-{
-	return ANGLE_1;
-}
diff --git a/src/g_shared/a_spark.cpp b/src/g_shared/a_spark.cpp
index c86d6600b1..18b27d9ff4 100644
--- a/src/g_shared/a_spark.cpp
+++ b/src/g_shared/a_spark.cpp
@@ -42,17 +42,11 @@ class ASpark : public AActor
 {
 	DECLARE_CLASS (ASpark, AActor)
 public:
-	angle_t AngleIncrements ();
 	void Activate (AActor *activator);
 };
 
 IMPLEMENT_CLASS (ASpark)
 
-angle_t ASpark::AngleIncrements ()
-{
-	return ANGLE_1;
-}
-
 void ASpark::Activate (AActor *activator)
 {
 	Super::Activate (activator);
diff --git a/src/p_mobj.cpp b/src/p_mobj.cpp
index 8332d489d2..ae376f1484 100644
--- a/src/p_mobj.cpp
+++ b/src/p_mobj.cpp
@@ -2614,11 +2614,6 @@ void AActor::RemoveFromHash ()
 	tid = 0;
 }
 
-angle_t AActor::AngleIncrements ()
-{
-	return ANGLE_45;
-}
-
 //==========================================================================
 //
 // AActor :: GetMissileDamage
@@ -3700,8 +3695,6 @@ void AActor::LevelSpawned ()
 {
 	if (tics > 0 && !(flags4 & MF4_SYNCHRONIZED))
 		tics = 1 + (pr_spawnmapthing() % tics);
-	angle_t incs = AngleIncrements ();
-	angle -= angle % incs;
 	flags &= ~MF_DROPPED;		// [RH] clear MF_DROPPED flag
 	HandleSpawnFlags ();
 }
@@ -3960,7 +3953,15 @@ APlayerPawn *P_SpawnPlayer (FMapThing *mthing, bool tempplayer)
 	{
 		spawn_x = mthing->x;
 		spawn_y = mthing->y;
-		spawn_angle = ANG45 * (mthing->angle/45);
+		// Allow full angular precision but avoid roundoff errors for multiples of 45 degrees.
+		if (mthing->angle % 45 != 0)
+		{
+			spawn_angle = mthing->angle * (ANG45 / 45);
+		}
+		else
+		{
+			spawn_angle = ANG45 * (mthing->angle / 45);
+		}
 	}
 
 	mobj = static_cast<APlayerPawn *>