After discussing the comparative effectiveness of different measures of dispersion used as indices of inequality, the Weighted Coefficient of Variation is proposed as an appropriate indicator of geographical inequality attending infant death. Furthermore, this paper proposes a methodology based on simple linear regression to be employed for the purposes of assessing the percentage of the observed change in said inequality over any given period, as is required by the terms of Target 1 of the WHO policy document "Health for All by the Year 2000". To this end, trends in Infant, Neonatal, Postneonatal and Perinatal Mortality in Spain for the period 1975-1986 have been analysed. For the 12 years examined, the Average Spanish Rate for these four indicators fell by over 50%. We observed a statistically significant decrease (34.8%) in geographical inequalities in the case of Postneonatal Mortality. However for the same period, geographical inequalities in Perinatal Mortality showed an important and significant rise (79.33%). It is suggested that, where Spain is concerned, it is Perinatal Mortality which should be assigned priority status for monitoring purposes. A plan of action should be drawn up, duly targeted at reducing geographical inequalities in health services, in the mother-and-child care sector above all.