Despite progress made in recent decades, infant and neonatal mortality rates (NMRs) in India have remained high compared to neighbouring developing countries. This study aims at establishing quantitative links between the relatively slow progress in fight against neonatal death at national level and strikingly varying mortality patterns at sub-national level. It appears that the tempo and quantum of reductions in neonatal mortality have been inconsistent across time, states, and urban and rural sub-populations. Decompositions have shown that the total NMR decrease in India, since the early 1980s has been largely driven by mortality changes in poorer states and rural areas, whereas compositional changes had negligible impact. The disparity in NMRs across the sub-populations which had been declining earlier stabilised in the 2000s. These disparities produce a heavy burden of avoidable death. While the mortality excess in poorer states and rural areas constitutes the core of bulk of excess deaths, some richer states, and urban areas, also show unexpected slower mortality decreases. However, the experience of the two states of Kerala and Tamil Nadu highlights the potential for declines in NMRs in low-income settings with sensible health and social policies.