[Andrew2]

The wire can be just dangling near the loop which would cause capacitive coupling, or you could form a single-turn loop in the wire (size equal to or less than the Tecsun size) and take the free end to an earth connection. This is inductive coupling and the new loop can be flipped around on its axis to reverse the phase. It's all very iffy while it's in this state, but I got results from my system fairly quickly. A good starting point is to listen to the radio and adjust the noise coupling until you hear the noise just increasing. This means the noise from the Tecsun and the noise from the wire antenna are about the same. Then you only have the phase adjustment to do.
My first system used a ferrite rod antenna and a tuning cap mounted together on a baseboard and a wire antenna loosely coupled (via a small cap) into the 'top end' of the tuned circuit. Phase reversal was by turning the entire rod ass'y around 180 degrees and fine phase by small twiddlings to the tuning cap. I think I later graduated to a single turn coupling coil on the rod for the wire antenna, which enabled me to reverse the phase by slipping the winding off the rod and flipping it around.
Things became a lot easier when I stopped mucking around and made a boxed, active unit with amplitude controls and phase reversal switches!
I'm sorry if my description is a bit dense, but explaining something makes you realise just what a complex thing you've been doing without thinking about it!