A poor night's sleep is almost guaranteed to negatively impact your day, but you don't have to get all your winks in one shot. Consider the "siesta" sleep method and other schedules to get in more quality shut-eye.
Designer Dustin Curtis chronicled his own battles for better sleep, concluding that "all you really need to survive and feel rested is the REM phase". He writes at his blog that the way to force your brain into this state is to trick it into thinking you're only going to have a tiny window of time to get your sleep on.
Specifically, he advocates going the polyphasic sleep route, a method that essentially trains the brain to enter REM for short periods of time via 20-minute naps, rather than through one long night of sleep. The post breaks down five polyphasic sleep options, the simplest of which is the "Siesta" method. This involves "just one nap in the day and then a huge chunk of sleep at night", which should shave one hour and 40 minutes off your total sleep requirements. Each method increases the number of total naps—"The Uberman" requires six 20-minute naps, for example—but each requires fairly strict adherence to the routine.
You can't miss a nap by more than a couple hours in the 2 and 3 "Everyman" methods, and you must have your naps within 30 minutes of their scheduled times for the Uberman method. If you miss a nap, the whole schedule is thrown off and you'll feel tired for days.
If you don't have the flexibile schedule needed to try out the Siesta and other listed methods, check out these less time-intensive ways to sleep smarter and better, and don't forget to select the right sleep posture once you have your plan in place.
How to Hack Your Brain, Part 1: Sleep [Dustin Curtis]