Byrne and Giordano bring Superman into the climax of the Shadow War storyline that had been the mainstay of Hawkman through specials, a miniseries, and his own book’s first year, in Action 588 (May 1987).
The story takes place between issues 10 and 11 of Hawkman, and sees Superman and the Hawks on their spaceship, surrounded by the Thanagarian fleet. Two of their adversaries are captive, Ved and Byth.
It is very much a middle chapter, but Byrne infuses it with plenty of action to keep it going.
Byth gets free, and uses his shape-changing powers to impersonate Hawkman, but Hawkwoman knows Katar would never attack her this way. She defeats and re-imprisons Byth.
Superman and Hawkman scatter the Thanagarian fleet through hyperspace, but Superman gets lost as well.
While the Hawks continue in their own book, Superman’s plot thread is picked up in the next issue of Action.