In my world, I have a very humanlike species that doesn't sleep. It's biologically impossible for these creatures to sleep, and for the sake of this question, assume that this species is exactly identical to modern humans except for the fact that they don't sleep. The members of the species do not enter any sort of state of sleep for any duration of time. However, this species does rest for short periods of time by staying stationary (but never enters a state of sleep while resting). By short periods of time, I mean resting about 4 hours each earth week.
Is this premise feasible? What changes in biochemistry, biology, or genetics would I have to make to make this more believable?