A couple of years ago I took all forms of 'time' out of my bedroom. Clock, alarm clock, radio etc, and it has made for a much better night's sleep.
There is no led display casting a glow in the room, nothing to tell me what time it is if I wake in the night and make me stressed about how long I've been awake or how soon I'll have to get up. If I can go back to sleep then I will and if not then I can read or get up... and knowing the time won't make a difference to either of those things.
There is no annoying ticking (I also take the batteries out of a downstairs clock I can hear from the bedroom) and nothing to startle me in the morning with big green glowing numbers and make me feel immediately guilty if I've overslept.
As long as I go to bed at a reasonable time (and it's got too late recently) then I'll sleep for around the same number of hours each night and wake at a suitable time in the morning. No stress, no guilt! And if I have to be up at a specific time then I'll either set a radio alarm on the landing that I can hear from the bedroom, or use an alarm on an old mobile phone that I can keep switched off during the night.
It just takes the pressure off. We're so conditioned to clock watch, and if there's no need then why stress about what time it is? It's surprising how quickly your body gets into its own rhythm. I haven't worn a watch for well over a decade either.
It might not work for everyone but it definitely lowers my stress levels. Why not try it for a few nights?