This book is from the perspective of Jack, a mage from a broken home who can't quite kick that smack addiction. Thirteen years ago, Jack made a deal with a demon, and now the time is nigh. He must break contract or be dragged into a hell with no escape. The novel begins with him lying and rationalizing his decision to lie. Let me make it clear: I did not like skinny junkie Jack in book one, and in book two he's worse (the front cover illustration is way off).
Apparently Pete (who is nearly 30 years old) quit her lifelong career as a police investigative detective to be with him, because suddenly they have a free-lancing business banishing ghosts that Jack couldn't give a flying *recurring-dated-British-slang-word* about. This is the beginning of story flow breakdown, because even though Pete is no longer policing, she regularly uses police resources because of 'old contacts'. I don't think it works that way, and I really didn't understand how end book one Pete transformed into book two Petunia.
Jack only cares about saving Pete from being associated with him, and he lies creatively to avoid facing reality. Lies catch up, and the author leaves an entire half-book storyline about a haunted house unresolved as Jack runs. He runs to Bangkok, where his old mentor Seth appears in a too-convenient fashion.
As for out-witting the demon, I found the ending a big dose of deus-ex handwaving, laid on especially thick slices of hell and destiny, for both Jack and Pete. The author decides arbitrarily which mythology trumps another throughout the book, is not consistent with regards to this, and by the ending, I thought Kittredge had no underlying theme. Bad world-building combined with being too gritty dramatically and not enough shown explanations (Jack tells Pete what things mean, but we know he is an unreliable narrator and liar) ruined the story flow. The only consistent theme I found was Jack screwing up Pete's life, and a steady stream of inventive sarcasm.
If rational logic is something you like in urban fantasy, if clear world-building is necessary for your stories, and if you don't like liars, you'll dislike Demon Bound. If what you want is a dose of spooky on the gritty side, a fast pace, a charming troublesome jerk who does magic tricks, and don't enjoy thinking about books, then you'll like it. Personally, I'm done with this author.