In a new sign of increasing inequality in the U.S., the richest 1% of Americans in 2006 garnered the highest share of the nation's adjusted gross income for two decades, and possibly the highest since 1929, according to Internal Revenue Service data.

Meanwhile, the average tax rate of the wealthiest 1% fell to its lowest level in at least 18 years. The group's share of the tax burden has risen, though not as quickly as its share of income.

The...