The United States Tax Court rejected a bid by the Internal Revenue Service to collect $3.9 million from the estate of the former Enron chief Kenneth L. Lay and his wife.

The case was related to transactions among Mr. Lay, his wife, Linda, and Enron that were executed on Sept. 21, 2001. The Lays sold $10 million in annuities to Enron as part of an agreement for him to retake the chief executive position, under the stipulation that the annuities would be returned to him if he worked a 4 ¼-year term. The company did not survive that long, and it filed for bankruptcy protection in December 2001.

The I.R.S. contested the Lays’ assertion that the annuities had been sold to Enron. In 2009, the I.R.S. filed a notice of tax deficiency for $3.9 million, arguing that the Lays should have reported the $10 million as income in 2001. Instead, they reported that they sold the annuities to Enron at their cost basis for no gain.

Judge Joseph Goeke of the tax court said in the decision that the agency’s position was incorrect and ruled for Mrs. Lay and for Mr. Lay’s estate. The transactions, he wrote, were legitimate, and neither of the Lays nor the estate received any distributions or death benefit from the annuity.