Should I use set once variables?

Question

Does this smell?
I have a few properties you can only set once. They can be set at any time during the objects existence and can not be undone.
I implement then like

Answer 1

Just make the setters methods and not properties - and the disconnect between expectation and behavior goes away. The method is free to throw an InvalidOperationException - but it's unexpected to have a property setter do it.

private FooThingy _foo;
public FooThingy Foo
{
    get { return _foo; }
}

public void SetFooThingy(FooThingy value) {
   if (Foo != null) 
      throw new InvalidOperationException("Foo is already set!");
   _foo = value;
}