Adding PostBackTriggers and AsyncPostBackTriggers to UpdatePanel for dynamically-generated grandchild controls

I have a page with a ScriptManager, a generic HTML drop-down list (<select>), and an UpdatePanel. The UpdatePanel contains a PlaceHolder (for now). During Page_Load, a number of user controls are added to the PlaceHolder (really, it’s several instances of the same user control). The number to add is not known until the page loads, so they do need to be loaded dynamically. The drop-down list is populated with the same number of menu items, and there is javascript on the page also (using jQuery) to show only one of the controls at a time depending on the state of the drop-down list.