Dilemma. How to fit a book into a recognised genre slot?

I am trying to work out where my new idea for a Single Title Book would be classified – by a literary agent, a publisher and  a bookseller.

MYSTERY? or ROMANCE?

Here are the key aspects of the idea:

* Contemporary city location – not small town

* The heroine is the amateur female detective trying to solve a puzzle which is very personal to her – while holding down a normal job in which she is skilled

* Witty but not laugh out loud dialogue and hero/heroine banter- intended to be a fun read. [Think Jenny Crusie and some Susan Elizabeth Phillips and Rachel Gibson etc.]

* Romantic – hero and heroine meet and form a relationship by the end of the book, but no closure

* No violence and medium sensuality rating – no detailed sex scenes for example.

* Intended to be first book in a series for this amateur female detective.

*Not a hard Romantic Suspense Novel aka Tami Hoag, Nora Roberts et al but more of a Light Crime Fun read.

At first I thought it would qualify as a Cozy Mystery but then no, more of a contemporary Single Title Romance with some amateur detective work as a plot device.  But not a Romantic Comedy.

I recall speaking to a UK literary agent several years ago and her view was that in the UK a light style of Romantic Suspense would definitely be pitched as a Romance, while in the US..?

Clearly a lot more research needed! LOL.