diff --git a/Lib/tkinter/simpledialog.py b/Lib/tkinter/simpledialog.py
index b882d47..638da87 100644
--- a/Lib/tkinter/simpledialog.py
+++ b/Lib/tkinter/simpledialog.py
@@ -55,36 +55,8 @@ def __init__(self, master,
                 b.config(relief=RIDGE, borderwidth=8)
             b.pack(side=LEFT, fill=BOTH, expand=1)
         self.root.protocol('WM_DELETE_WINDOW', self.wm_delete_window)
-        self._set_transient(master)
-
-    def _set_transient(self, master, relx=0.5, rely=0.3):
-        widget = self.root
-        widget.withdraw() # Remain invisible while we figure out the geometry
-        widget.transient(master)
-        widget.update_idletasks() # Actualize geometry information
-        if master.winfo_ismapped():
-            m_width = master.winfo_width()
-            m_height = master.winfo_height()
-            m_x = master.winfo_rootx()
-            m_y = master.winfo_rooty()
-        else:
-            m_width = master.winfo_screenwidth()
-            m_height = master.winfo_screenheight()
-            m_x = m_y = 0
-        w_width = widget.winfo_reqwidth()
-        w_height = widget.winfo_reqheight()
-        x = m_x + (m_width - w_width) * relx
-        y = m_y + (m_height - w_height) * rely
-        if x+w_width > master.winfo_screenwidth():
-            x = master.winfo_screenwidth() - w_width
-        elif x < 0:
-            x = 0
-        if y+w_height > master.winfo_screenheight():
-            y = master.winfo_screenheight() - w_height
-        elif y < 0:
-            y = 0
-        widget.geometry("+%d+%d" % (x, y))
-        widget.deiconify() # Become visible at the desired location
+        self.root.transient(master)
+        _place_window(self.root, master)
 
     def go(self):
         self.root.wait_visibility()
@@ -157,11 +129,7 @@ def __init__(self, parent, title = None):
 
         self.protocol("WM_DELETE_WINDOW", self.cancel)
 
-        if parent is not None:
-            self.geometry("+%d+%d" % (parent.winfo_rootx()+50,
-                                      parent.winfo_rooty()+50))
-
-        self.deiconify() # become visible now
+        _place_window(self, parent)
 
         self.initial_focus.focus_set()
 
@@ -251,6 +219,37 @@ def apply(self):
         pass # override
 
 
+# Place a toplevel window at the center of parent or screen
+# It is a Python implementation of ::tk::PlaceWindow.
+def _place_window(w, parent=None):
+    w.wm_withdraw() # Remain invisible while we figure out the geometry
+    w.update_idletasks() # Actualize geometry information
+
+    minwidth = w.winfo_reqwidth()
+    minheight = w.winfo_reqheight()
+    maxwidth = w.winfo_vrootwidth()
+    maxheight = w.winfo_vrootheight()
+    if parent is not None and parent.winfo_ismapped():
+        x = parent.winfo_rootx() + (parent.winfo_width() - minwidth) // 2
+        y = parent.winfo_rooty() + (parent.winfo_height() - minheight) // 2
+        vrootx = w.winfo_vrootx()
+        vrooty = w.winfo_vrooty()
+        x = min(x, vrootx + maxwidth - minwidth)
+        x = max(x, vrootx)
+        y = min(y, vrooty + maxheight - minheight)
+        y = max(y, vrooty)
+        if w._windowingsystem == 'aqua':
+            # Avoid the native menu bar which sits on top of everything.
+            y = max(y, 22)
+    else:
+        x = (w.winfo_screenwidth() - minwidth) // 2
+        y = (w.winfo_screenheight() - minheight) // 2
+
+    w.wm_maxsize(maxwidth, maxheight)
+    w.wm_geometry('+%d+%d' % (x, y))
+    w.wm_deiconify() # Become visible at the desired location
+
+
 # --------------------------------------------------------------------
 # convenience dialogues