In any ranking of high-profile U.S. Supreme Court cases, last month’s arguments over same-sex marriage would be hard to beat.

But the next and final argument cycle of this Supreme Court term is looking like a headline-grabber as well.

A potentially landmark gene-patenting case that was featured on the CBS program 60 Minutes in 2010 will be argued April 15. And the Baby Veronica case, an Indian adoption dispute that attracted the interest of Dr. Phil and Anderson Cooper last year, will be argued the next day. Add a number of criminal law cases and the First Amendment, and the high court will be ending its argument season with a bang.

If you haven’t heard much about these cases in the past few weeks, though, you can chalk it up to what Gregory Castanias calls "media fatigue" caused by the intense spotlight on the same-sex arguments.

That is not affecting Castanias’ preparations for argument in Association for Molecular Pathology v. Myriad Genetics Inc. The Jones Day partner heads the firm’s practice at the U.S. Court of Appeals for the Federal Circuit, where he argued and won support for Myriad’s controversial patents for genes associated with breast and ovarian cancer. But in keeping with Jones Day’s long-standing policy of spreading Supreme Court work around, Castanias will argue at the Supreme Court as well.

Although intellectual property has been "the principal focus" of his practice, Castanias said he is not a specialist in the sense of being a scientist, and he won’t get too bogged down in technical details. "I majored in English and philosophy," he said.

Castanias, who is appearing for his fourth time before the high court, will argue that the company’s patents are valid, protecting an inventive process that entailed an "enormous amount of human judgment," not just isolating something that exists in nature.

On the other side will be Christopher Hansen, senior national staff counsel at the American Civil Liberties Union. A 40-year veteran of the ACLU, Hansen has appeared only once before the high court, in the 1991 arguments in the Freeman v. Pitts school-desegregation case. "This is the first patent case ever brought by the ACLU," said staff attorney Sandra Park in a recent interview with the Breast Cancer Action group. "We studied the issue closely and consulted with many people before deciding to get involved. Ultimately, we realized that gene patents…must be challenged because of the important civil liberties concerns they raise."

The ACLU argues that patents unfairly allow owners to block innovation by locking up research and use of the genes. The United States, which filed an amicus brief on neither side, will also get argument time. Solicitor General Donald Verrilli Jr. will argue that some but not all gene patents are inappropriate.

A wide range of amici have filed in the case, including James Watson, one half of the Watson-Crick team that discovered the structure of DNA 60 years ago. Watson will be in the courtroom to watch the arguments. Watson’s brief, authored by Matthew Dowd of Wiley Rein, argues that genes should not be patented — but if they are, fair access should be guaranteed through licensing. Later Monday, Wiley Rein will host a panel discussion featuring Watson and others, including Paul Michel, retired chief judge of the Federal Circuit.

The Adoptive Couple v. Baby Girl case set for April 16 tests the Indian Child Welfare Act, passed in 1978 to preserve Native American families. In custody battles, the law gives highest priority to keeping the child in the care of Indian parents and tribes whenever possible — a requirement that in this instance and others can clash with the "best interests of the child" standard otherwise used to resolve such disputes.

The lineup of advocates arguing in the Indian case and the following week is a testament to the dominance of Supreme Court veterans in arguments these days.

Three of the lawyers appearing — Lisa Blatt, arguing for the adoptive couple; Paul Clement, who represents the guardian ad litem in support of the adoptive couple; and Mayer Brown’s Charles Rothfeld, who represents the Cherokee tribe and the father — will have second arguments later in the cycle. Once upon a time, arguing one case per term was rare for a lawyer; now, it is almost old hat for veteran lawyers to have two arguments within a two-week cycle.

Clement, a partner at the Bancroft firm, will argue again on April 23 for the petitioner in Sekhar v. U.S., a Hobbs Act case. The next day, Rothfeld will represent the water district in Tarrant Regional Water District v. Herrmann, a water rights dispute. And Arnold & Porter’s Blatt will represent the other side in the Tarrant case.

Speaking of Blatt, her two arguments in April will put her ahead again in the friendly competition for most cases ever argued by a woman before the Supreme Court. She and Patricia Millett of Akin Gump Strauss Hauer & Feld trade the title back and forth. Millett is for the moment in the lead with 32 Supreme Court arguments to her name, and Blatt 31. But Blatt’s April will put her ahead with 33.

Coming off his confirmation hearing last week, principal deputy solicitor general Sri Srinivasan will appear before the court April 22 to defend a federal law that requires groups receiving funds for overseas AIDS programs to adopt policies opposing prostitution and sex trafficking.

In Agency for International Development v. Alliance for Open Society International, the law is being challenged on First Amendment grounds as an improper condition on government funding. David Bowker of Wilmer Cutler Pickering Hale and Dorr will argue for the challengers who assert that a forced policy could alienate host countries and hamper groups’ efforts to organize and assist sex workers.

The court hears two cases on the criminal side on April 17. First up is U.S. v. Kebodeaux, a test of whether the federal sex-offender registration requirement applies to those whose prison terms were completed before the law took effect in 2006. Representing Anthony Kebodeaux will be M. Carolyn Fuentes, assistant federal public defender in the Western District of Texas.

Next, Salinas v. Texas asks whether the Fifth Amendment protects a defendant’s refusal to answer police questions before being arrested or being read the Miranda warning. Stanford Law School professor Jeffrey Fisher will argue for petitioner Genovevo Salinas.

Tony Mauro can be contacted at tmauro@alm.com.