"This Case Had More Holes in It Than a Swiss Cheese and More Loose Ends Than a Torn String Vest"

"The Case of the Four and Twenty Blackbirds."
By Neil Gaiman (born 1960).
First appearance in Knave (U.K.), 1984.
Collected in Angels and Visitations - A Miscellany (1993) and The Mammoth Book of Comic Fantasy II (1999), among others.
Short story (~16 pages).
Online HERE.

"Then she gave me a lopsided smile that would have made Albert Einstein drop a decimal point."

For some PIs, cases just seem to throw themselves at you:

I sat in my office, nursing a glass of hooch and idly cleaning my automatic. Outside the rain fell steadily, like it seems to do most of the time in our fair city, whatever the tourist board says. Hell, I didn't care. I'm not on the tourist board. I'm a private dick, and one of the best, although you wouldn't have known it; the office was crumbling, the rent was unpaid and the hooch was my last.

Things are tough all over.

To cap it all the only client I'd had all week never showed up on the street corner where I'd waited for him. He said it was going to be a big job, but now I'd never know: he kept a prior appointment in the morgue.

So when the dame walked into my office I was sure my luck had changed for the better.

"What are you selling, lady?"

She gave me a look that would have induced heavy breathing in a pumpkin, and which shot my heartbeat up to three figures. She had long blonde hair and a figure that would have made Thomas Aquinas forget his vows. I forgot all mine about never taking cases from dames.  . . .

Another author has explored the same literary terrain at greater length (see HERE), but Gaiman was there first.

Resources:
- Wikipedia HERE, FictionMags HERE, and the ISFDb HERE.

The bottom line: 

  'And how exactly like an egg he is!' she said aloud, standing with her hands ready to catch him, for she was every moment expecting him to fall.
   — Through the Looking-Glass (And What Alice Found There)