The Beatles legend, who attended a private hearing at London's High Court last week, was seen giving a two-fingered "victory" sign as he emerged from court and believes the case is going his way.
The two-day hearing examined Heather's claims that Paul was physically violent towards her during their four-year marriage.
Paul's lawyers are said to have produced a "truth and lies" document which examined each of Heather's claims which they believe cemented their arguments that the former model is a "fantasist."
A source said: "Paul had prepared a dossier to prove beyond all reasonable doubt that Heather is a liar."
"They went through every single utterance she has made and scrutinized them thoroughly."
The document allegedly caused such concern for Heather's lawyers that she was advised to agree to a settlement.
The hearing also examined Heather's maintenance and security costs.
Heather, 39 - who has received death threats since the couple split last May - has reportedly demanded round-the-clock security Paul, 64, insists he should only provide security when Heather is with their three-year-old daughter Beatrice.
