problems with meditation in the morning

I have problems meditating in the morning. I usually feel very tired when getting up early on a weekday and then have a limited timeframe (~ 30 min.) for meditation. My body feels so tired, that I am unable to meditate. This is often accompanied by the tendency to get into a negative, rejecting mindstate. Should I try to meditate anyway or try to bring up energy (going outside, cold shower)? Is it possible to influence the habitual tiredness in the morning (at least a bit), or is this exclusively a body thing?