WASHINGTON -- The Supreme Court appears likely to rule for an inmate on Texas' death row who was denied money to investigate his history of mental illness and other claims that could spare him from being executed.

The case the justices heard Monday involves an immigrant from Honduras who was sentenced to death for strangling a woman in her home in Houston.

The immigrant's lawyers for his appeals in the federal court system determined that his trial and state appellate lawyers did not do enough to look into the man's past in search of mitigating evidence that might persuade a jury not to impose a death sentence.

But federal courts refused a request for money to investigate, despite a federal law aimed at improving legal representation in capital cases.