Primary research question: For pregnant women with non-severe, non-proteinuric maternal hypertension at 14-33 weeks, will 'less tight' control (target diastolic blood pressure [dBP] of 100 mmHg) versus 'tight' control (target dBP of 85 mmHg) increase (or decrease) the likelihood of pregnancy loss or Neonatal Intensive Care Unit (NICU) admission for greater than 48 hours? Secondary research question: Will 'less tight' versus 'tight' control increase (or decrease) the likelihood of serious maternal complications? Other research questions: Will 'less tight' versus 'tight' control: 1. Increase (or decrease) the likelihood of serious perinatal complications? 2. Increase (or decrease) the likelihood of severe hypertension and pre-eclampsia? 3. Increase (or decrease) the likelihood of maternal satisfaction with care? 4. Result in significant changes in dBP or health care costs? Treatment Allocation: Eligible women will be randomised centrally to either 'less tight' control (aiming for dBP of 100mmHg) or 'tight' control (aiming for dBP of 85mmHg) of their hypertension. Randomisation will be stratified by centre and type of hypertension (pre-existing or gestational). - In the 'less tight' control group, if dBP is ≥105mmHg, then antihypertensive medication must be started or increased in dose. - In the 'tight' control group, if dBP is ≤80mmHg, then antihypertensive medication must be decreased in dose or discontinued. - In both groups, centres will provide their usual care. Data will be collected on potential co-interventions (e.g., hospitalisation, bedrest). Outcomes: Primary: Pregnancy loss (miscarriage or ectopic pregnancy, pregnancy termination, stillbirth, or neonatal death) or high level neonatal care for >48 hours in the first 28 days of life or prior to primary hospital discharge, whichever is later. Secondary: One/more serious maternal complication(s) until six weeks postpartum. Follow-up: Compliance (dBP and antihypertensive dose) will be assessed within 4 weeks of randomisation. Outcome data will be collected during the woman's (and baby's) hospital stay for birth (or loss). Women will be contacted 6 to 12 weeks after delivery (or loss) and, for preterm babies, when the baby is at 36 weeks corrected gestational age to enquire about satisfaction with care and any major maternal/neonatal morbidity following hospital discharge. The investigators do not know which approach to treatment of non-severe high blood pressure in pregnancy is better for women and babies. In the CHIPS Trial, the investigators seek to determine whether 'less tight' control (aiming for a diastolic blood pressure [dBP] of 100 mmHg), compared with 'tight' control (aiming for a diastolic blood pressure [dBP] of 85 mmHg) can decrease the risks of adverse baby outcomes without increasing the risk of problems for the mother.