To "get an inch of sleep" refers to, plainly, getting a little bit of sleep. The term was made popular by the ever-enlightening, world renowned scientologist, Jacqui.
"Guys, shut the hell up, I can't get an inch of sleep with you people screaming!"

*fart noise*

*next morning*

"I didn't get an inch of sleep last night!"
by c.ingach January 30, 2006
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