diff --git a/static/js/popover_menus.js b/static/js/popover_menus.js
index 8daa918a3a..0854d8a1fe 100644
--- a/static/js/popover_menus.js
+++ b/static/js/popover_menus.js
@@ -3,7 +3,7 @@
    popovers system in popovers.js. */
 
 import $ from "jquery";
-import {delegate} from "tippy.js";
+import tippy, {delegate} from "tippy.js";
 
 import render_compose_control_buttons_popover from "../templates/compose_control_buttons_popover.hbs";
 import render_compose_select_enter_behaviour_popover from "../templates/compose_select_enter_behaviour_popover.hbs";
@@ -67,10 +67,39 @@ function on_show_prep(instance) {
     popovers.hide_all_except_sidebars(instance);
 }
 
+function tippy_no_propagation(target, popover_props) {
+    // For some elements, such as the click target to open the message
+    // actions menu, we want to avoid propagating the click event to
+    // parent elements. Tippy's built-in `delegate` method does not
+    // have an option to do stopPropagation, so we use this method to
+    // open the Tippy popovers associated with such elements.
+    //
+    // A click on the click target will close the menu; for this to
+    // work correctly without leaking, all callers need call
+    // `instance.destroy()` inside their `onHidden` handler.
+    //
+    // TODO: Should we instead we wrap the caller's `onHidden` hook,
+    // if any, to add `instance.destroy()`?
+    $("body").on("click", target, (e) => {
+        e.preventDefault();
+        e.stopPropagation();
+        const instance = e.currentTarget._tippy;
+
+        if (instance) {
+            instance.hide();
+            return;
+        }
+
+        tippy(e.currentTarget, {
+            ...default_popover_props,
+            showOnCreate: true,
+            ...popover_props,
+        });
+    });
+}
+
 export function initialize() {
-    delegate("body", {
-        ...default_popover_props,
-        target: "#streams_inline_icon",
+    tippy_no_propagation("#streams_inline_icon", {
         onShow(instance) {
             const can_create_streams =
                 settings_data.user_can_create_private_streams() ||
@@ -90,12 +119,15 @@ export function initialize() {
             left_sidebar_stream_setting_popover_displayed = true;
             return true;
         },
-        onHidden() {
+        onHidden(instance) {
+            instance.destroy();
             left_sidebar_stream_setting_popover_displayed = false;
         },
     });
 
     // compose box buttons popover shown on mobile widths.
+    // We want this click event to propagate and hide other popovers
+    // that could possibly obstruct user from using this popover.
     delegate("body", {
         ...default_popover_props,
         target: ".compose_mobile_button",
@@ -135,9 +167,7 @@ export function initialize() {
     // Click event handlers for it are handled in `compose_ui` and
     // we don't want to close this popover on click inside it but
     // only if user clicked outside it.
-    delegate("body", {
-        ...default_popover_props,
-        target: ".compose_control_menu_wrapper",
+    tippy_no_propagation(".compose_control_menu_wrapper", {
         placement: "top",
         onShow(instance) {
             instance.setContent(
@@ -150,14 +180,13 @@ export function initialize() {
             compose_control_buttons_popover_instance = instance;
             popovers.hide_all_except_sidebars(instance);
         },
-        onHidden() {
+        onHidden(instance) {
+            instance.destroy();
             compose_control_buttons_popover_instance = undefined;
         },
     });
 
-    delegate("body", {
-        ...default_popover_props,
-        target: ".enter_sends",
+    tippy_no_propagation(".enter_sends", {
         placement: "top",
         onShow(instance) {
             on_show_prep(instance);