diff --git a/dlls/winex11.drv/window.c b/dlls/winex11.drv/window.c
index 59affca1b1d..06ce26ed2e4 100644
--- a/dlls/winex11.drv/window.c
+++ b/dlls/winex11.drv/window.c
@@ -2404,6 +2404,16 @@ void CDECL X11DRV_WindowPosChanged( HWND hwnd, HWND insert_after, UINT swp_flags
     release_win_data( data );
 }
 
+/* check if the window icon should be hidden (i.e. moved off-screen) */
+static BOOL hide_icon( struct x11drv_win_data *data )
+{
+    static const WCHAR trayW[] = {'S','h','e','l','l','_','T','r','a','y','W','n','d',0};
+
+    if (data->managed) return TRUE;
+    /* hide icons in desktop mode when the taskbar is active */
+    if (root_window == DefaultRootWindow( gdi_display )) return FALSE;
+    return IsWindowVisible( FindWindowW( trayW, NULL ));
+}
 
 /***********************************************************************
  *           ShowWindow   (X11DRV.@)
@@ -2418,18 +2428,18 @@ UINT CDECL X11DRV_ShowWindow( HWND hwnd, INT cmd, RECT *rect, UINT swp )
     struct x11drv_thread_data *thread_data = x11drv_thread_data();
     struct x11drv_win_data *data = get_win_data( hwnd );
 
-    if (!data || !data->whole_window || !data->managed) goto done;
+    if (!data || !data->whole_window) goto done;
     if (IsRectEmpty( rect )) goto done;
     if (style & WS_MINIMIZE)
     {
-        if (rect->left != -32000 || rect->top != -32000)
+        if (((rect->left != -32000 || rect->top != -32000)) && hide_icon( data ))
         {
             OffsetRect( rect, -32000 - rect->left, -32000 - rect->top );
             swp &= ~(SWP_NOMOVE | SWP_NOCLIENTMOVE);
         }
         goto done;
     }
-    if (!data->mapped || data->iconic) goto done;
+    if (!data->managed || !data->mapped || data->iconic) goto done;
 
     /* only fetch the new rectangle if the ShowWindow was a result of a window manager event */