Why let Leamas and Nan escape?

The Spy Who Came In From The Cold is one of my all time favorite movies, and I've seen it half a dozen times by now, but there's one part that always seemed a little sketchy. At the end of the movie, Leamas is let out of his cell by Mundt and provided with a car. Mundt also lets Leamas' lover, Nan, escape with him. Mundt knows, however, that Leamas is going to tell Nan everything, which is why he has the boy shoot her as she and Leamas are climbing over the wall. When Leamas sees that Nan has been shot, he decides that he doesn't want to go on living without her, climbs back to the East German side, and gets shot.

Why was Nan released in the first place, however? Leamas seems to believe, in his final monologue, that it was part of a deal, and that Mundt believed that he wouldn't leave without her, a belief that is justified in the last minute of the film. But it seems to me that Leamas would be more likely to accept life as a Nan-less spy if she was ditched in East Germany than if she was shot by a fellow British agent. Furthermore, a more convincing argument for his return could have been made by Mundt at the gate than the one Smiley and the boy attempt to make in the last lines of the film.

It would also have been better for Mundt to keep Nan in East Germany, because it makes the escape less suspicious. The Soviets will easily believe that Fiedler's co-conspirators helped Leamas escape, because Leamas was working for them and they owed it to him, and the official explanation is that Leamas and Fiedler were working together to incriminate Mundt, so it makes sense that Fiedler's friends would help him escape. What makes less sense, however, is Fiedler's friends helping Nan escape - they owe nothing to her, and Nan was the girl who unraveled their entire plot. They have no motive for saving her other than that Leamas wants them to, and that motive is non-consequential enough that the story Mundt will provide would make sense without letting Nan go.

So why was Nan let go? Is there another reason I'm missing, or am I mixing up a motive somewhere?