diff --git a/qml/Main.qml b/qml/Main.qml
index 8803474..4e01631 100644
--- a/qml/Main.qml
+++ b/qml/Main.qml
@@ -36,6 +36,9 @@ Window {
     visible: false
     color: "transparent"
 
+    // Alt+F4 or the task manager would hide it behind the visibility
+    // controller's back; the dismiss key and the tray toggle hide it instead.
+    onClosing: close => close.accepted = false
     onInputRegionChanged: placement?.setInputRegion(inputRegion)
     onBlurRegionChanged: placement?.setBlurRegion(blurRegion, Theme.windowRadius)
     // For CollapseController.
diff --git a/src/main.cpp b/src/main.cpp
index c9ac594..2d4cb59 100644
--- a/src/main.cpp
+++ b/src/main.cpp
@@ -157,6 +157,8 @@ int main(int argc, char *argv[])
     // libwayland unsets it once connected.
     const bool launchedByKWin = qEnvironmentVariableIsSet("WAYLAND_SOCKET");
     QGuiApplication app(argc, argv);
+    // KWin relaunches it only after a crash: a closed window mustn't quit it.
+    QGuiApplication::setQuitOnLastWindowClosed(false);
     quitOnSignal();
     QGuiApplication::setApplicationName(QStringLiteral("sloposk"));
     QGuiApplication::setOrganizationName(QStringLiteral("sloposk")); // ~/.config/sloposk/sloposk.conf
diff --git a/src/window/VisibilityController.cpp b/src/window/VisibilityController.cpp
index 31240d5..062e836 100644
--- a/src/window/VisibilityController.cpp
+++ b/src/window/VisibilityController.cpp
@@ -26,6 +26,13 @@ void VisibilityController::setAlwaysVisible(bool always)
     update();
 }
 
+void VisibilityController::setEnabled(bool enabled)
+{
+    m_enabled = enabled;
+    m_override.reset();
+    update();
+}
+
 void VisibilityController::show()
 {
     m_override = true;
@@ -46,7 +53,8 @@ void VisibilityController::toggle()
 
 void VisibilityController::update()
 {
-    const bool visible = m_override.value_or(m_alwaysVisible || m_standalone || (m_fieldActive && m_showOnField));
+    const bool visible =
+        m_enabled && m_override.value_or(m_alwaysVisible || m_standalone || (m_fieldActive && m_showOnField));
     if (visible == m_visible)
         return;
     m_visible = visible;
diff --git a/src/window/VisibilityController.h b/src/window/VisibilityController.h
index a32020d..d72862b 100644
--- a/src/window/VisibilityController.h
+++ b/src/window/VisibilityController.h
@@ -9,6 +9,7 @@
 //    standalone (no input-method connection)
 //  - show()/hide()/toggle() override that until the focus changes, also
 //    from one field straight to another
+//  - never while the system's virtual keyboard toggle is off
 class VisibilityController : public QObject
 {
     Q_OBJECT
@@ -24,6 +25,8 @@ public:
     void setShowOnField(bool show);
     void setStandalone(bool standalone);
     void setAlwaysVisible(bool always);
+    // The system toggle (KWin's tray icon); off hides it whatever else says.
+    void setEnabled(bool enabled);
 
     void show();
     void hide();
@@ -39,6 +42,7 @@ private:
     bool m_showOnField = true;
     bool m_standalone = false;
     bool m_alwaysVisible = false;
+    bool m_enabled = true;
     std::optional<bool> m_override;
     bool m_visible = false;
 };
diff --git a/tests/tst_visibility.cpp b/tests/tst_visibility.cpp
index c37c836..693e84d 100644
--- a/tests/tst_visibility.cpp
+++ b/tests/tst_visibility.cpp
@@ -70,6 +70,19 @@ private Q_SLOTS:
         QVERIFY(!v.isVisible());
     }
 
+    void systemToggleGatesEverything()
+    {
+        VisibilityController v;
+        v.setAlwaysVisible(true);
+        v.setEnabled(false);
+        QVERIFY(!v.isVisible());
+        v.show();
+        QVERIFY(!v.isVisible());
+        v.hide();
+        v.setEnabled(true); // turning it back on forgets the dismiss
+        QVERIFY(v.isVisible());
+    }
+
     void standaloneAlwaysVisible()
     {
         VisibilityController v;