diff --git a/plugins/ui/src/js/src/ObjectView.tsx b/plugins/ui/src/js/src/ObjectView.tsx
index 987068ef5..5a6f4eb95 100644
--- a/plugins/ui/src/js/src/ObjectView.tsx
+++ b/plugins/ui/src/js/src/ObjectView.tsx
@@ -13,7 +13,11 @@ function ObjectView(props: ObjectViewProps) {
   const { object } = props;
   log.info('Object is', object);
 
-  const fetch = useCallback(() => object.fetch() as Promise<Widget>, [object]);
+  const fetch = useCallback(async () => {
+    // We reexport the object in case this object is used in multiplate places or closed/opened multiple times
+    const reexportedObject = await object.reexport();
+    return reexportedObject.fetch() as Promise<Widget>;
+  }, [object]);
 
   const plugins = usePlugins();
 
diff --git a/plugins/ui/src/js/src/UITable.tsx b/plugins/ui/src/js/src/UITable.tsx
index 7106650b8..d1f971df5 100644
--- a/plugins/ui/src/js/src/UITable.tsx
+++ b/plugins/ui/src/js/src/UITable.tsx
@@ -19,12 +19,20 @@ function UITable({ element }: UITableProps) {
 
   // Just load the object on mount
   useEffect(() => {
+    let isCancelled = false;
     async function loadModel() {
       log.debug('Loading table from props', element.props);
-      const newTable = (await element.props.table.fetch()) as Table;
+      const reexportedTable = await element.props.table.reexport();
+      const newTable = (await reexportedTable.fetch()) as Table;
+      if (isCancelled) {
+        newTable.close();
+      }
       setTable(newTable);
     }
     loadModel();
+    return () => {
+      isCancelled = true;
+    };
   }, [dh, element]);
 
   const irisGridProps: Partial<IrisGridProps> = useMemo(() => {
diff --git a/plugins/ui/src/js/src/WidgetHandler.tsx b/plugins/ui/src/js/src/WidgetHandler.tsx
index cb2283dd4..9f2df8dfb 100644
--- a/plugins/ui/src/js/src/WidgetHandler.tsx
+++ b/plugins/ui/src/js/src/WidgetHandler.tsx
@@ -160,6 +160,10 @@ function WidgetHandler({ onClose, widget: wrapper }: WidgetHandlerProps) {
     if (widget == null) {
       return;
     }
+    // Need to reset the exported object map and count
+    const widgetExportedObjectMap = new Map<number, WidgetExportedObject>();
+    exportedObjectMap.current = widgetExportedObjectMap;
+    exportedObjectCount.current = 0;
     function receiveData(
       data: string,
       newExportedObjects: WidgetExportedObject[]
@@ -184,8 +188,14 @@ function WidgetHandler({ onClose, widget: wrapper }: WidgetHandlerProps) {
     receiveData(widget.getDataAsString(), widget.exportedObjects);
 
     return () => {
-      log.debug('Cleaning up listener');
+      log.debug('Cleaning up widget', widget);
       cleanup();
+      widget.close();
+
+      // Clean up any exported objects that haven't been closed yet
+      Array.from(widgetExportedObjectMap.values()).forEach(exportedObject => {
+        exportedObject.close();
+      });
     };
   }, [dh, jsonClient, parseDocument, updateExportedObjects, widget]);
 
@@ -194,9 +204,12 @@ function WidgetHandler({ onClose, widget: wrapper }: WidgetHandlerProps) {
       log.debug('loadWidget', wrapper.id, wrapper.definition);
       let isCancelled = false;
       async function loadWidgetInternal() {
-        const newWidget = await wrapper.fetch(false);
+        const newWidget = await wrapper.fetch();
         if (isCancelled) {
           newWidget.close();
+          newWidget.exportedObjects.forEach(exportedObject => {
+            exportedObject.close();
+          });
           return;
         }
         log.debug('newWidget', wrapper.id, wrapper.definition, newWidget);
@@ -210,14 +223,6 @@ function WidgetHandler({ onClose, widget: wrapper }: WidgetHandlerProps) {
     [wrapper]
   );
 
-  useEffect(
-    () =>
-      function closeWidget() {
-        widget?.close();
-      },
-    [widget]
-  );
-
   const handleDocumentClose = useCallback(() => {
     log.debug('Widget document closed', wrapper.id);
     onClose?.(wrapper.id);