Back in the nineties, I worked for a big company where lots of people wanted to work. We had what I called "resume reading parties". A half-dozen of us, managers and ICs, would sit around a pile of resumes in the middle and start reading. When we finished each one we would check either "Y" or "N" and pass the resume to our left...except two noes and the resume was put in the reject pile. Sometimes they fed us. From there would be phone screening then on-site interviews. HR didn't like being cut out of the loop but we knew we were better at screening than they were.

A benefit of this process is that your resume-writing skills improve a lot. Read a hundred or so resumes and you'll learn what catches your eye and what gets ignored.

Alas, nobody else does this. I used to mention this process at places I worked but people thought I was nuts. It worked, though. We rarely had a hire that didn't work out.