Eros at Zenith, second in the "Tales of the Velvet Comet" series by Mike Resnick.
[The flap copy from the Phantasia hc]: The Velvet Comet, the most luxurious brothel in the galaxy, functions as a haven from mundane care, a retreat from everyday reality. It is an exotic place of fantasy and masks - until murder rears its ugly head, and one by one the masks are stripped away from the various players in Mike Resnick's latest novel. And beneath those masks are a truly memorable set of characters:
The Black Pearl, a madam who finds herself the unwilling defender of a man whose mere presence can destroy the Velvet Comet;
Andrew Jackson Crane, a detective whose uncontrolled ambition can spell doom to everyone around him;
The Dragon Lady, a Security Chief who is torn between her loyalties and her judgement;
Pagliacci, a rather unfunny comedian with a rather unfunny secret;
Quintus Bello, a man who has possibly committed the most heinous crime of the century;
And Cupid, a computer that cannot originate ideas. Probably...