What is Spade's ulterior motive in helping out Brigid?

Spade and Brigid both are putting up fronts so that their behavior will not be construed as suspicious, but each has an ulterior motive. Spade is duplicitous in that he would profit nicely by turning the falcon over to Cairo, but he maintains the facade that he is helping Brigid. By doing this, he garners some nice personal perks on the side.