diff --git a/src/p_pspr.cpp b/src/p_pspr.cpp
index b9ba6b932..0f01522d1 100644
--- a/src/p_pspr.cpp
+++ b/src/p_pspr.cpp
@@ -143,7 +143,7 @@ DPSprite::DPSprite(player_t *owner, AInventory *caller, int id)
 		Next->Destroy(); // Replace it.
 
 	if (Caller->IsKindOf(RUNTIME_CLASS(AWeapon)))
-		Flags = (PSPF_ADDWEAPON|PSPF_ADDBOB);
+		Flags = (PSPF_ADDWEAPON|PSPF_ADDBOB|PSPF_POWDOUBLE|PSPF_CVARFAST);
 }
 
 //------------------------------------------------------------------------
@@ -210,6 +210,10 @@ DPSprite *player_t::GetPSprite(PSPLayers layer)
 
 	if (newcaller != oldcaller)
 	{ // Only change the flags if this layer was created now or if we updated the caller.
+		if (layer >= PSP_TARGETCENTER)
+		{ // The targeter layers were affected by those.
+			pspr->Flags |= (PSPF_CVARFAST|PSPF_POWDOUBLE);
+		}
 		if (layer != PSP_FLASH)
 		{ // Only the flash layer should follow the weapon.
 			pspr->Flags &= ~PSPF_ADDWEAPON;
@@ -286,7 +290,7 @@ void DPSprite::SetState(FState *newstate, bool pending)
 
 		Tics = newstate->GetTics(); // could be 0
 
-		if (Caller->IsKindOf(RUNTIME_CLASS(AWeapon)))
+		if (Flags & PSPF_CVARFAST)
 		{
 			if (sv_fastweapons == 2 && ID == PSP_WEAPON)
 				Tics = newstate->ActionFunc == nullptr ? 0 : 1;
@@ -1358,7 +1362,7 @@ void DPSprite::Tick()
 			Tics--;
 
 			// [BC] Apply double firing speed.
-			if (Caller->IsKindOf(RUNTIME_CLASS(AWeapon)) && Tics && Owner->cheats & CF_DOUBLEFIRINGSPEED)
+			if ((Flags & PSPF_POWDOUBLE) && Tics && (Owner->cheats & CF_DOUBLEFIRINGSPEED))
 				Tics--;
 
 			if (!Tics)
diff --git a/src/p_pspr.h b/src/p_pspr.h
index c3400f43d..9ef3208e5 100644
--- a/src/p_pspr.h
+++ b/src/p_pspr.h
@@ -55,6 +55,8 @@ enum PSPFlags
 {
 	PSPF_ADDWEAPON	= 1 << 0,
 	PSPF_ADDBOB		= 1 << 1,
+	PSPF_POWDOUBLE	= 1 << 2,
+	PSPF_CVARFAST	= 1 << 3,
 };
 
 class DPSprite : public DObject
diff --git a/wadsrc/static/actors/constants.txt b/wadsrc/static/actors/constants.txt
index d65e9e463..4bd2dc199 100644
--- a/wadsrc/static/actors/constants.txt
+++ b/wadsrc/static/actors/constants.txt
@@ -575,6 +575,8 @@ enum
 {
 	PSPF_ADDWEAPON	= 1 << 0,
 	PSPF_ADDBOB		= 1 << 1,
+	PSPF_POWDOUBLE	= 1 << 2,
+	PSPF_CVARFAST	= 1 << 3,
 };
 
 // Default psprite layers