To catch some ZZZZ's means to get some sleep. According to The Facts on File Encyclopedia of Word and Phrase Origins, this phrase traces its origins to the common use of the 'ZZZZ' or 'zzzz' in cartoons to indicate a sleeping character.
|An example of 'Z' indicating sleep - note the final panel.|
Though I am no longer dosing with medication at odd hours, I still have bouts of fatigue that just demand that I am frequently dozing at odd hours. I absolutely refuse to take any sleep aids. One doctor recommended (and was rather upset when I refused) that I do so in order to restore a more normal sleep schedule. I just didn't think that I needed any sort of pharmaceutical assistance with it. The last thing that I want to do it to become dependent on a drug for something as natural as sleep. The further recommendation to take a stimulant in the morning so that I could stay awake through the day and 'would be tired at an appropriate time' cemented my decision to avoid drug-assisted sleep.