Integration Services :: Adding Values To A Drop Down List In Custom SSIS Task

I am writing my first custom SSIS task and I can see that, if I put a public property into the task, I see that property in the standard Properties window. If I add a property of type String, I can put a value in that property, in the task code, and when I instantiate the task in a package, I can see the value I entered.

To try and get a drop down list property in the Properties window, I declared a property of type Combobox, and indeed a drop down list appears in that property.

My problem is trying to get values in that property. I have used the test items:

    Property.Items.add("Fred")
    Property.Items.Add("Jim")

But I do not see the values in the drop down list. All I do see is one item with a value of "(none)".