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

Set-once-properties violate the principle of least surprise - a caller expects that when a property can be set once, it can be set again. (barring range and compatibility checks, of course - but they are bound to specific values or value combinations).

Initialize them in the constructor.
Alternatively, if they are to many / to complex to write all constructors, use a factory/builder class:

ThingieBuilder tb = new ThingieBuilder();
tb.FooThingy = 17.23;   // r/w properties
tb.BarThingy = 42;
tb.UseExtendedThingamagicAdapter = true;
Thingie t = tb.Create();
if (t.Bar==42) // r/o property
  ...

Or, separate the settings in a configuration object, that can be replaced or passed during construction.

Answer 2

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;
}