diff --git a/src/p_mobj.cpp b/src/p_mobj.cpp
index e70f3cc0a..955672c67 100644
--- a/src/p_mobj.cpp
+++ b/src/p_mobj.cpp
@@ -3879,7 +3879,7 @@ AActor *AActor::StaticSpawn (const PClass *type, fixed_t ix, fixed_t iy, fixed_t
 		actor->SpawnPoint[2] = (actor->z - actor->floorz);
 	}
 
-	actor->FloatBobPhase = rng();	// Don't make everything bob in sync
+	if (actor->FloatBobPhase < 0) actor->FloatBobPhase = rng();	// Don't make everything bob in sync (unless deliberately told to do)
 	if (actor->flags2 & MF2_FLOORCLIP)
 	{
 		actor->AdjustFloorClip ();
diff --git a/src/thingdef/thingdef_properties.cpp b/src/thingdef/thingdef_properties.cpp
index e3461792b..662c868ee 100644
--- a/src/thingdef/thingdef_properties.cpp
+++ b/src/thingdef/thingdef_properties.cpp
@@ -624,6 +624,16 @@ DEFINE_PROPERTY(scale, F, Actor)
 	defaults->scaleX = defaults->scaleY = id;
 }
 
+//==========================================================================
+//
+//==========================================================================
+DEFINE_PROPERTY(floatbobphase, F, Actor)
+{
+	PROP_FIXED_PARM(id, 0);
+	if (id < -1 || id >= 64) I_Error ("FloatBobPhase must be in range [-1,63]");
+	defaults->FloatBobPhase = id;
+}
+
 //==========================================================================
 //
 //==========================================================================
diff --git a/wadsrc/static/actors/actor.txt b/wadsrc/static/actors/actor.txt
index 8e76ca374..950521361 100644
--- a/wadsrc/static/actors/actor.txt
+++ b/wadsrc/static/actors/actor.txt
@@ -16,6 +16,7 @@ ACTOR Actor native //: Thinker
 	WallBounceFactor 0.75
 	BounceCount -1
 	FloatSpeed 4
+	FloatBobPhase -1	// randomly initialize by default
 	Gravity 1
 	DamageFactor 1.0
 	PushFactor 0.25