diff --git a/conversejs/custom/plugins/tasks/muc-task-lists-view.js b/conversejs/custom/plugins/tasks/muc-task-lists-view.js
index 58cf9af9..8b436f5a 100644
--- a/conversejs/custom/plugins/tasks/muc-task-lists-view.js
+++ b/conversejs/custom/plugins/tasks/muc-task-lists-view.js
@@ -112,9 +112,11 @@ export default class MUCTaskListsView extends CustomElement {
   }
 
   _handleDragStart (ev) {
-    if (!this._isATaskEl(ev.target)) { return }
+    // The draggable=true is on a livechat-converse-muc-task child
+    const possibleTaskEl = ev.target.parentElement
+    if (!this._isATaskEl(possibleTaskEl)) { return }
     console.log('Starting to drag a task...')
-    this.currentDraggedTask = ev.target
+    this.currentDraggedTask = possibleTaskEl
     this._resetDropOver()
   }
 
diff --git a/conversejs/custom/plugins/tasks/templates/muc-task-list.js b/conversejs/custom/plugins/tasks/templates/muc-task-list.js
index e6def70e..70b22a89 100644
--- a/conversejs/custom/plugins/tasks/templates/muc-task-list.js
+++ b/conversejs/custom/plugins/tasks/templates/muc-task-list.js
@@ -67,7 +67,7 @@ export default function tplMucTaskList (el, tasklist) {
       ${el.collapsed
         ? ''
         : repeat(tasks, (task) => task.get('id'), (task) => {
-          return html`<livechat-converse-muc-task .model=${task} draggable="true"></livechat-converse-muc-task>`
+          return html`<livechat-converse-muc-task .model=${task}></livechat-converse-muc-task>`
         })
       }
     </div>
diff --git a/conversejs/custom/plugins/tasks/templates/muc-task.js b/conversejs/custom/plugins/tasks/templates/muc-task.js
index d3f8f69a..f869394e 100644
--- a/conversejs/custom/plugins/tasks/templates/muc-task.js
+++ b/conversejs/custom/plugins/tasks/templates/muc-task.js
@@ -9,7 +9,7 @@ export function tplMucTask (el, task) {
   const doneId = 'livechat-task-done-id-' + task.get('id')
   return !el.edit
     ? html`
-      <div class="task-line" ?task-is-done=${done}>
+      <div draggable="true" class="task-line" ?task-is-done=${done}>
         <div class="form-check">
           <input
             id="${doneId}"