diff --git a/CMakeLists.txt b/CMakeLists.txt
index bf636b5..9143fbc 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -22,7 +22,7 @@ qt_add_executable(tncat
 target_include_directories(tncat PRIVATE src)
 
 # QML files live in qml/ but register at the module root (TNCat.Main etc.)
-set(TNCAT_QML Main Cat Chip Cup CatWindow ChipWindow CupWindow OverlayWindow
+set(TNCAT_QML Main Desktop Cat Chip Cup CatWindow ChipWindow CupWindow OverlayWindow
                SettingsWindow AppButton AppSlider AppToggle SettingsGroup CatDefs)
 foreach(qmlfile IN LISTS TNCAT_QML)
     set_source_files_properties(qml/${qmlfile}.qml PROPERTIES QT_RESOURCE_ALIAS ${qmlfile}.qml)
diff --git a/qml/Desktop.qml b/qml/Desktop.qml
new file mode 100644
index 0000000..fa4d168
--- /dev/null
+++ b/qml/Desktop.qml
@@ -0,0 +1,31 @@
+pragma ComponentBehavior: Bound
+import QtQuick
+import TNCat
+
+// The layout for platforms that let a client place its own window: one small
+// window per object, moved around the screen by the app.
+QtObject {
+    id: desktop
+
+    required property CatController cat
+    required property AppSettings settings
+
+    signal settingsRequested()
+
+    readonly property CatWindow catWindow: CatWindow {
+        cat: desktop.cat
+        settings: desktop.settings
+        visible: true
+        onSettingsRequested: desktop.settingsRequested()
+    }
+
+    readonly property ChipWindow chipWindow: ChipWindow {
+        cat: desktop.cat
+        settings: desktop.settings
+    }
+
+    readonly property CupWindow cupWindow: CupWindow {
+        cat: desktop.cat
+        settings: desktop.settings
+    }
+}
diff --git a/qml/Main.qml b/qml/Main.qml
index b590384..70820b3 100644
--- a/qml/Main.qml
+++ b/qml/Main.qml
@@ -2,7 +2,9 @@ pragma ComponentBehavior: Bound
 import QtQuick
 import TNCat
 
-// Root is not a window: which windows exist depends on the platform.
+// Root is not a window. Exactly one of the two layouts is built, because both
+// of them drive the controller's catCenter; having both alive made the two
+// bindings overwrite each other every frame and the eyes jumped with them.
 QtObject {
     id: app
 
@@ -15,30 +17,23 @@ QtObject {
         settingsWindow.requestActivate()
     }
 
-    readonly property CatWindow catWindow: CatWindow {
-        cat: app.cat
-        settings: app.settings
-        visible: !Platform.overlayMode
-        onSettingsRequested: app.openSettings()
+    readonly property Loader desktopLoader: Loader {
+        active: !Platform.overlayMode
+        sourceComponent: Desktop {
+            cat: app.cat
+            settings: app.settings
+            onSettingsRequested: app.openSettings()
+        }
     }
 
-    readonly property ChipWindow chipWindow: ChipWindow {
-        cat: app.cat
-        settings: app.settings
-        visible: !Platform.overlayMode && app.cat.chipVisible
-    }
-
-    readonly property CupWindow cupWindow: CupWindow {
-        cat: app.cat
-        settings: app.settings
-        visible: !Platform.overlayMode && app.cat.cupVisible
-    }
-
-    readonly property OverlayWindow overlayWindow: OverlayWindow {
-        cat: app.cat
-        settings: app.settings
-        overlayActive: Platform.overlayMode
-        onSettingsRequested: app.openSettings()
+    readonly property Loader overlayLoader: Loader {
+        active: Platform.overlayMode
+        sourceComponent: OverlayWindow {
+            cat: app.cat
+            settings: app.settings
+            overlayActive: true
+            onSettingsRequested: app.openSettings()
+        }
     }
 
     readonly property SettingsWindow settingsWindow: SettingsWindow {