As recently discussed on openjfx-dev [1], it would be helpful in some cases to disallow users to iconify their stage / window. At present there is an iconified property used to specified whether the stage is currently minimized down into the users task bar area, but there is no means to remove the minimize button from the titlebar area of the stage. This would be useful in cases such as dialogs. Various suggestions were given in the openjfx-dev thread, so it may be worth reviewing there for ideas. The two front-runners in terms of suggestions was to either provide fine-grained access to the stage buttons via an enum and a means of passing in a varargs list of which buttons are allowed, or alternatively via adding an iconifiable property that states whether a stage can be minimized.

[1] http://mail.openjdk.java.net/pipermail/openjfx-dev/2013-July/008948.html