diff --git a/src/add-ons/decorators/SATDecorator/StackAndTile.cpp b/src/add-ons/decorators/SATDecorator/StackAndTile.cpp
index 3c0f360804..8c35123435 100644
--- a/src/add-ons/decorators/SATDecorator/StackAndTile.cpp
+++ b/src/add-ons/decorators/SATDecorator/StackAndTile.cpp
@@ -113,7 +113,7 @@ StackAndTile::WindowRemoved(Window* window)
 }
 
 
-void
+bool
 StackAndTile::KeyPressed(uint32 what, int32 key, int32 modifiers)
 {
 	// switch to and from stacking and snapping mode
@@ -126,7 +126,83 @@ StackAndTile::KeyPressed(uint32 what, int32 key, int32 modifiers)
 			_StartSAT();
 	}
 
-	return;
+	if (!SATKeyPressed() || what != B_KEY_DOWN)
+		return false;
+
+	const int kArrowKeyUp = 87;
+	const int kArrowKeyDown = 98;
+
+	switch (key) {
+		case kArrowKeyDown:
+		{
+			SATWindow* frontWindow = GetSATWindow(fDesktop->FocusWindow());
+			SATGroup* currentGroup = NULL;
+			if (frontWindow)
+				currentGroup = frontWindow->GetGroup();
+			if (currentGroup && currentGroup->CountItems() <= 1)
+				currentGroup = NULL;
+
+			GroupIterator groups(this, fDesktop);
+			bool currentFound = false;
+			while (true) {
+				SATGroup* group = groups.NextGroup();
+				if (group == NULL)
+					break;
+				if (group->CountItems() <= 1)
+					continue;
+
+				if (currentGroup == NULL)
+					currentFound = true;
+						// if no group is selected just activate the first one
+				else if (currentGroup == group) {
+					currentFound = true;
+					continue;
+				}
+				if (currentFound) {
+					_ActivateWindow(group->WindowAt(0));
+					if (currentGroup) {
+						Window* window = currentGroup->WindowAt(0)->GetWindow();
+						fDesktop->SendWindowBehind(window);
+						WindowSentBehind(window, NULL);
+					}
+					return true;
+				}
+			}
+			break;
+		}
+
+		case kArrowKeyUp:
+		{
+			SATWindow* frontWindow = GetSATWindow(fDesktop->FocusWindow());
+			SATGroup* currentGroup = NULL;
+			if (frontWindow)
+				currentGroup = frontWindow->GetGroup();
+			if (currentGroup && currentGroup->CountItems() <= 1)
+				currentGroup = NULL;
+
+			SATGroup* backmostGroup = NULL;
+			GroupIterator groups(this, fDesktop);
+			while (true) {
+				SATGroup* group = groups.NextGroup();
+				if (group == NULL)
+					break;
+				if (group->CountItems() <= 1)
+					continue;
+				// if no group is selected just activate the first one
+				if (currentGroup == NULL) {
+					_ActivateWindow(group->WindowAt(0));
+					return true;
+				}
+				backmostGroup = group;
+			}
+			if (backmostGroup && backmostGroup != currentGroup) {
+				_ActivateWindow(backmostGroup->WindowAt(0));
+				return true;
+			}
+			break;
+		}
+	}
+	return false;
 }
 
 
@@ -369,6 +445,9 @@ StackAndTile::GetDecoratorSettings(Window* window, BMessage& settings)
 SATWindow*
 StackAndTile::GetSATWindow(Window* window)
 {
+	if (window == NULL)
+		return NULL;
+
 	SATWindowMap::const_iterator it = fSATWindowMap.find(
 		window);
 	if (it != fSATWindowMap.end())
diff --git a/src/add-ons/decorators/SATDecorator/StackAndTile.h b/src/add-ons/decorators/SATDecorator/StackAndTile.h
index cd0ba9361f..18b125c219 100644
--- a/src/add-ons/decorators/SATDecorator/StackAndTile.h
+++ b/src/add-ons/decorators/SATDecorator/StackAndTile.h
@@ -54,7 +54,7 @@ public:
 	virtual void				WindowAdded(Window* window);
 	virtual void				WindowRemoved(Window* window);
 	
-	virtual void				KeyPressed(uint32 what, int32 key,
+	virtual bool				KeyPressed(uint32 what, int32 key,
 									int32 modifiers);
 	virtual void				MouseEvent(BMessage* message) {}
 	virtual void				MouseDown(Window* window, BMessage* message,
diff --git a/src/servers/app/Desktop.cpp b/src/servers/app/Desktop.cpp
index 934137466c..370400e874 100644
--- a/src/servers/app/Desktop.cpp
+++ b/src/servers/app/Desktop.cpp
@@ -221,9 +221,7 @@ KeyboardFilter::Filter(BMessage* message, EventTarget** _target,
 		|| message->what == B_INPUT_METHOD_EVENT)
 		_UpdateFocus(key, modifiers, _target);
 
-	fDesktop->KeyEvent(message->what, key, modifiers);
-
-	return B_DISPATCH_MESSAGE;
+	return fDesktop->KeyEvent(message->what, key, modifiers);
 }
 
 
@@ -578,7 +576,7 @@ Desktop::BroadcastToAllWindows(int32 code)
 }
 
 
-void
+filter_result
 Desktop::KeyEvent(uint32 what, int32 key, int32 modifiers)
 {
 	if (LockAllWindows()) {
@@ -594,7 +592,10 @@ Desktop::KeyEvent(uint32 what, int32 key, int32 modifiers)
 		UnlockAllWindows();
 	}
 
-	NotifyKeyPressed(what, key, modifiers);
+	if (NotifyKeyPressed(what, key, modifiers))
+		return B_SKIP_MESSAGE;
+
+	return B_DISPATCH_MESSAGE;
 }
 
 
diff --git a/src/servers/app/Desktop.h b/src/servers/app/Desktop.h
index 077c60d0fe..3bc22d2d6b 100644
--- a/src/servers/app/Desktop.h
+++ b/src/servers/app/Desktop.h
@@ -72,7 +72,7 @@ public:
 			void				BroadcastToAllApps(int32 code);
 			void				BroadcastToAllWindows(int32 code);
 
-			void				KeyEvent(uint32 what, int32 key,
+			filter_result		KeyEvent(uint32 what, int32 key,
 									int32 modifiers);
 	// Locking
 			bool				LockSingleWindow()
diff --git a/src/servers/app/DesktopListener.cpp b/src/servers/app/DesktopListener.cpp
index 6580663145..84599c5ab1 100644
--- a/src/servers/app/DesktopListener.cpp
+++ b/src/servers/app/DesktopListener.cpp
@@ -91,16 +91,20 @@ DesktopObservable::NotifyWindowRemoved(Window* window)
 }
 
 
-void
+bool
 DesktopObservable::NotifyKeyPressed(uint32 what, int32 key, int32 modifiers)
 {
 	if (fWeAreInvoking)
-		return;
+		return false;
 	InvokeGuard invokeGuard(fWeAreInvoking);
 
+	bool skipEvent = false;
 	for (DesktopListener* listener = fDesktopListenerList.First();
-		listener != NULL; listener = fDesktopListenerList.GetNext(listener))
-		listener->KeyPressed(what, key, modifiers);
+		listener != NULL; listener = fDesktopListenerList.GetNext(listener)) {
+		if (listener->KeyPressed(what, key, modifiers))
+			skipEvent = true;
+	}
+	return skipEvent;
 }
 
 
diff --git a/src/servers/app/DesktopListener.h b/src/servers/app/DesktopListener.h
index a8aceeb049..df102a5399 100644
--- a/src/servers/app/DesktopListener.h
+++ b/src/servers/app/DesktopListener.h
@@ -38,7 +38,7 @@ public:
 	virtual void				WindowAdded(Window* window) = 0;
 	virtual void				WindowRemoved(Window* window) = 0;
 
-	virtual void				KeyPressed(uint32 what, int32 key,
+	virtual bool				KeyPressed(uint32 what, int32 key,
 									int32 modifiers) = 0;
 	virtual void				MouseEvent(BMessage* message) = 0;
 	virtual void				MouseDown(Window* window, BMessage* message,
@@ -92,7 +92,7 @@ public:
 			void				NotifyWindowAdded(Window* window);
 			void				NotifyWindowRemoved(Window* window);
 
-			void				NotifyKeyPressed(uint32 what, int32 key,
+			bool				NotifyKeyPressed(uint32 what, int32 key,
 									int32 modifiers);
 			void				NotifyMouseEvent(BMessage* message);
 			void				NotifyMouseDown(Window* window,