diff --git a/CHANGES.rst b/CHANGES.rst
index 0ca1283..bd80a99 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -3,6 +3,7 @@ CHANGE HISTORY
 
 LATEST
 ------
+- Added border option to PopupMenu
 
 1.15.0
 ------
diff --git a/asciimatics/widgets/popupmenu.py b/asciimatics/widgets/popupmenu.py
index 2af4780..c5fe5e2 100644
--- a/asciimatics/widgets/popupmenu.py
+++ b/asciimatics/widgets/popupmenu.py
@@ -16,21 +16,27 @@ class PopupMenu(Frame):
     palette = defaultdict(lambda: (Screen.COLOUR_WHITE, Screen.A_NORMAL, Screen.COLOUR_CYAN))
     palette["focus_button"] = (Screen.COLOUR_CYAN, Screen.A_NORMAL, Screen.COLOUR_WHITE)
 
-    def __init__(self, screen, menu_items, x, y):
+    def __init__(self, screen, menu_items, x, y, has_border=False):
         """
         :param screen: The Screen being used for this pop-up.
         :param menu_items: a list of items to be displayed in the menu.
         :param x: The X coordinate for the desired pop-up.
         :param y: The Y coordinate for the desired pop-up.
+        :param has_border: Whether the menu has a border box. Defaults to False.
 
         The menu_items parameter is a list of 2-tuples, which define the text to be displayed in
         the menu and the function to call when that menu item is clicked.  For example:
 
             menu_items = [("Open", file_open), ("Save", file_save), ("Close", file_close)]
         """
+
+        border_adjustment = 0
+        if has_border:
+            border_adjustment = 2 # We add one character to each side for the border
+
         # Sort out location based on width of menu text.
-        w = max(len(i[0]) for i in menu_items)
-        h = len(menu_items)
+        w = max(len(i[0]) for i in menu_items) + border_adjustment
+        h = len(menu_items) + border_adjustment
         if x + w >= screen.width:
             x -= w - 1
         if y + h >= screen.height:
@@ -38,7 +44,7 @@ def __init__(self, screen, menu_items, x, y):
 
         # Construct the Frame
         super().__init__(
-            screen, h, w, x=x, y=y, has_border=False, can_scroll=False, is_modal=True, hover_focus=True)
+            screen, h, w, x=x, y=y, has_border=has_border, can_scroll=False, is_modal=True, hover_focus=True)
 
         # Build the widget to display the time selection.
         layout = Layout([1], fill_frame=True)
diff --git a/tests/test_widgets.py b/tests/test_widgets.py
index 81e2190..87f2bab 100644
--- a/tests/test_widgets.py
+++ b/tests/test_widgets.py
@@ -2905,6 +2905,73 @@ def click(x):
         self.assertEqual(len(scene.effects), 0)
         self.assertEqual(self.clicked, 2)
 
+        # Reset menu for border test
+        self.clicked = 0
+        popup = PopupMenu(canvas,
+                          [
+                              ("First", lambda: click(1)),
+                              ("Second", lambda: click(2)),
+                              ("Third", lambda: click(4))
+                          ],
+                          0, 0, has_border=True)
+        scene.add_effect(popup)
+        scene.reset()
+
+        # Check that the menu is rendered correctly.
+        for effect in scene.effects:
+            effect.update(0)
+        self.assert_canvas_equals(
+            canvas,
+            "+------+                                \n" +
+            "|First |                                \n" +
+            "|Second|                                \n" +
+            "|Third |                                \n" +
+            "+------+                                \n" +
+            "                                        \n" +
+            "                                        \n" +
+            "                                        \n" +
+            "                                        \n" +
+            "                                        \n")
+
+        # Check it handles a selection as expected
+        self.process_mouse(scene, [(1, 2, MouseEvent.LEFT_CLICK)])
+        self.assertEqual(len(scene.effects), 0)
+        self.assertEqual(self.clicked, 2)
+
+        # Reset menu for border and title test
+        self.clicked = 0
+        popup = PopupMenu(canvas,
+                          [
+                              ("First", lambda: click(1)),
+                              ("Second Wider", lambda: click(2)),
+                              ("Third", lambda: click(4))
+                          ],
+                          0, 0, has_border=True)
+        popup.title = 'Test'
+        scene.add_effect(popup)
+        scene.reset()
+
+        # Check that the menu is rendered correctly.
+        for effect in scene.effects:
+            effect.update(0)
+        self.assert_canvas_equals(
+            canvas,
+            "+--- Test ---+                          \n" +
+            "|First       |                          \n" +
+            "|Second Wider|                          \n" +
+            "|Third       |                          \n" +
+            "+------------+                          \n" +
+            "                                        \n" +
+            "                                        \n" +
+            "                                        \n" +
+            "                                        \n" +
+            "                                        \n")
+
+        # Check it handles a selection as expected
+        self.process_mouse(scene, [(1, 2, MouseEvent.LEFT_CLICK)])
+        self.assertEqual(len(scene.effects), 0)
+        self.assertEqual(self.clicked, 2)
+
         # Check choice of location at bottom right
         self.clicked = 0
         canvas.reset()