diff --git a/lib/extension/tree.js b/lib/extension/tree.js
index ea957d29..903457af 100644
--- a/lib/extension/tree.js
+++ b/lib/extension/tree.js
@@ -125,7 +125,9 @@ export class Node extends GObject.Object {
       case NODE_TYPES.MONITOR:
       case NODE_TYPES.ROOT:
       case NODE_TYPES.WORKSPACE:
-        if (this.actor) {
+        // (a container split off a window that was never laid out gets no rect until the next
+        // render, #540)
+        if (this.actor && rect) {
           this.actor.set_size(rect.width, rect.height);
           this.actor.set_position(rect.x, rect.y);
         }
diff --git a/lib/extension/window.js b/lib/extension/window.js
index 61820e1e..8335489d 100644
--- a/lib/extension/window.js
+++ b/lib/extension/window.js
@@ -1408,7 +1408,11 @@ export class WindowManager extends GObject.Object {
    */
   trackWindow(_display, metaWindow) {
     let autoSplit = this.ext.settings.get_boolean("auto-split-enabled");
-    if (autoSplit && this.focusMetaWindow) {
+    // Only for a window that is new to the tree: trackCurrentWindows() re-tracks every window
+    // after a workspace is added or removed, and splitting again for each of them wrapped the
+    // focused window in one more container each time (#540)
+    const isNewWindow = this._validWindow(metaWindow) && !this.tree.findNode(metaWindow);
+    if (autoSplit && isNewWindow && this.focusMetaWindow) {
       let currentFocusNode = this.tree.findNode(this.focusMetaWindow);
       if (currentFocusNode) {
         let currentParentFocusNode = currentFocusNode.parentNode;