This study revisits the well-known Kuznets hypothesis that postulated an inverted-U relation between the level of development of a country or region and its degree of income inequality. We address the widely-shared view that, in recent years, a regular-U, and not a Kuznets-type inverted-U, has characterized the relation between income and inequality in the United States and some other developed countries. The paper works with data for the US states and has two main distinguishing features. First, it permits cross-state spillovers, which seem conceptually relevant and statistically significant, but, to our knowledge, have not been included in the fairly extensive literature on the topic. Second, we use the most reliable recent annual panel covering the period 2006-2016, which has also not been included in any existing research. The pooled-OLS, as well as the two-way fixed-effects panel estimates, indicate the existence of a significant regular-U pattern which is consistent with the influential view in the literature. However, the estimates that adjust for cross-state spillovers indicate a weak regular-U pattern in which the (log) linear and quadratic terms lack statistical significance at the usual levels. We conclude that when cross-state spillovers are appropriately accounted for, statistically significant evidence is lacking to support the view that a regular-U pattern describes the relation between income and inequality in the United States in recent years.