The annex merely lists negotiating positions and proposals, and they are entirely notional: The parties may agree, for example, “that measures relating to entry, temporary stay and work of service providers are administered in a reasonable, objective and transparent manner.”

Protectionists say the mere existence of this annex reveals that Mr. Obama will use his trade promotion powers to sneak his immigration preferences through Congress. But keep in mind that none of this is even in the bill the House is considering this week. The current trade-promotion bill merely says that any deal Mr. Obama negotiates will get an up or down vote in Congress.

Congress is not giving up its right to reject a bad trade deal, and the fast-track bill includes a procedure that allows either chamber to “strip” trade promotion authority if the executive branch does not follow certain rules or attempts to cut out Congress. The House is even adding an amendment that bans any Administration from submitting trade deals that change immigration policy.