Next month the Supreme Court will start October Term 2015, and while most of the cases they take are important, some are more important than others. Probably in part because of the Roberts Court’s incrementalism, many of the cases require the high court to clean up unresolved issues in previous decisions. I’ll start with the cases to watch that they have already agreed to hear. At the bottom, I’ll mention some upcoming cases that the Court hasn’t taken yet, but should.

1. Hurst v. Florida, to be argued October 13.

Hurst is an Eighth Amendment case, testing whether Florida’s capital punishment regime, which allows judges and not juries to make factual findings about aggravating circumstances. Those findings can then be used to impose a death sentence, even if they’re never tried before a jury. There’s no such thing as a sure thing, but if you’re betting, bet that Florida’s capital punishment statute does not survive the term.

2. Montgomery v. Louisiana, also to be argued October 13.

In this criminal case, the high court must decide whether its 2012 decision in Miller v. Alabama applies retroactively. Miller struck down automatic life-without-the-possibility-of-parole sentences for juveniles as a violation of the Eighth Amendment. Montgomery got an automatic LWOP sentence in 1963, when he was seventeen years old, after conviction for the murder of a sheriff’s deputy. The case has the potential to continue the modern trend of nibbling away at harsh criminal sentencing laws.

3. Evenwel v. Abbott, argument date not set.

This redistricting case out of Texas will test the longstanding principle of “one person, one vote.” The issue is whether, consistent with the Equal Protection clause, states may apportion districts according to a “one voter, one vote” model rather than the “one person (even a noncitizen or a felon), one vote”. This has major implications for the balance of electoral power between rural and urban areas, as I explained in more detail over at Ace of Spades HQ back in May.

4. Fisher v. University of Texas at Austin, argument date not set.

This is the second iteration of an Equal Protection lawsuit filed by a white, would-be UT student who believes she was denied admission because of the university’s race-conscious application program. The Supreme Court dodged squarely answering whether the university’s affirmative action program withstands Equal Protection scrutiny in its 2013 decision. That question is back before the high court.

5. Friedrichs v. California Teachers Association, argument date not set.

In this labor law case, the Supreme Court is called on to answer the question it failed to reach in last term’s Harris v. Quinn: can public employees be compelled to pay fees to a union? In 1977, the high court held that mandatory fair share payments for public employee unions were constitutional. The conservative wing of the court practically begged for a case that would tee up an opportunity to overturn that holding, and they got it in this California case. The justices will also consider whether requiring public employees to opt out of paying for political speech, rather than allowing them to affirmatively opt in, violates the First Amendment.

Cert petitions to watch for.

The Supreme Court will continue to accept new cases throughout the term, but here are the one’s that would make good candidates.

First, let’s consider the Obamacare cases. A group of nuns, about which we have written much before, are asking the justices to take their case, Little Sisters of the Poor v. Burwell, challenging the contraception mandate accommodation as a violation of the Religious Freedom Restoration Act. (I explain RFRAs here.) The nuns contend that having to fill out the form to get the accommodation violates their religious conscience because it triggers the third-party provision of the very contraception coverage they object to. There’s a circuit split on this issue now owing to a case out of Missouri, Sharpe Holdings v. HHS, so we’re likely to see the Supreme Court take up one or both cases.

Second, there’s another important religious freedom case, Listecki v. Official Committee of Unsecured Creditors, about whether the federal RFRA can be used as a shield against any litigant or only against government action. The circuit courts are split on this, but they’ve been split for some time. There is some mild urgency on this question in light of last spring’s shenanigans with respect to RFRAs in Indiana, Arkansas, and North Carolina. More on that here.

Third, the Supreme Court is being asked to take up abortion once again. The case out of Mississippi is Currier v. Jackson Women’s Health Organization, which involves an abortion reform law placing requirements on physicians that would essentially close the state’s only abortion clinic. Another abortion reform law out of Texas, HB 2, was largely upheld by the Fifth Circuit, but a petition for review of that decision has not been filed yet. Either could be a vehicle for the high court to address whether states may impose safety-minded reforms on abortion clinics that end up forcing them out of business for inability to comply.

Finally, depending on how long the Fifth Circuit takes to rule on it, we may see President Obama’s deferred action program for the alien parents of U.S. citizen children at the Supreme Court this term. That program is currently on hold pending the litigation over whether it was lawful or constitutional for the Secretary of Homeland Security to announce a program of non-enforcement of the immigration laws.