There is wide variability in the use of prophylactic cyclooxygenase inhibitor (COX-I) drugs to prevent morbidity and mortality in preterm infants. Parents of preterm infants are rarely involved in this decision-making process. To explore the health-related values and preferences of adults who were preterm infants and families of preterm infants concerning the prophylactic use of indomethacin, ibuprofen, and acetaminophen initiated within the first 24 hours after birth. This cross-sectional study used direct choice experiments conducted in 2 phases of virtual video-conferenced interviews between March 3, 2021, and February 10, 2022: (1) a pilot feasibility study and (2) a formal study of values and preferences, using a predefined convenience sample. Participants included adults born very preterm (gestational age <32 weeks) or parents of very preterm infants currently in the neonatal intensive care unit (NICU) or having graduated from the NICU in the last 5 years. Relative importance of clinical outcomes, willingness to use each of the COX-Is when presented as the only option, preference for using prophylactic hydrocortisone vs indomethacin, willingness to use any of the COX-Is when all 3 options are available, and relative importance of having family values and preferences included in decision-making. Of 44 participants enrolled, 40 were included in the formal study (31 parents and 9 adults born preterm). The median gestational age of the participant or the participant's child at birth was 26.0 (IQR, 25.0-28.8) weeks. Death (median score, 100 [IQR, 100-100]) and severe intraventricular hemorrhage (IVH) (median score, 90.0 [IQR, 80.0-100]) were rated as the 2 most critical outcomes. Based on direct choice experiments, most participants were willing to consider prophylactic indomethacin (36 [90.0%]) or ibuprofen (34 [85.0%]), but not acetaminophen (4 [10.0%]) when offered as the only option. Among participants who initially chose indomethacin (n = 36), if prophylactic hydrocortisone was offered as a potential therapy with the caveat that both cannot be used simultaneously, only 12 of 36 (33.3%) preferred to remain with indomethacin. Variability in preference was noted when all 3 COX-I options were available, indomethacin (19 [47.5%]) being the most preferred option followed by ibuprofen (16 [40.0%]), while the remainder opted for no prophylaxis (5 [12.5%]). The findings of this cross-sectional study of former preterm infants and parents of preterm infants suggest that there was minimal variability in how participants valued the main outcomes, with death and severe IVH being rated as the 2 most important undesirable outcomes. While indomethacin was the most preferred form of prophylaxis, variability was noted in the choice of COX-I interventions when participants were presented with the benefits and harms of each drug.