There is an abstract in the journal Hypertension from August 2011 about the relationship between sleep stages and development of high blood pressure (a.k.a. HTN). There are three stages of sleep - light non-REM sleep, deep sleep, and REM (a.k.a. dream) sleep. Researchers studied 784 men greater than 64 years old who did not have HTN with an in-home sleep study. After a mean follow up of 3.4 years, 243 developed HTN. Analyses of the results demonstrated that developing HTN was associated with low oxygen levels, increased light non-REM sleep, and decreased deep sleep. After adjusting for age, nonwhite race, study site, and body mass index, only deep sleep was associated with developing HTN. The association was not reduced even after accounting for sleep duration, sleep fragmentation, and severity of sleep-disordered breathing (e.g. obstructive sleep apnea).
The researchers concluded that reduced deep sleep may contribute to adverse blood pressure in men. Unfortunately, the percentage of sleep that is deep sleep normally reduces with age in men and women. At the current moment, there is not a reliable way to increase deep sleep percentage without sleep deprivation or using medications.