HUNTSVILLE, Texas -- An employee at the Lubbock city landfill spotted a brand-new piece of luggage amid the mountain of trash, opened the suitcase and discovered the beaten naked body of a 29-year-old woman stuffed inside.

Detectives used a barcode label sewn to the luggage to establish it was purchased a day earlier at a Walmart. Debit card records and store surveillance video identified the buyer as Rosendo Rodriguez III, a Marine reservist from San Antonio who'd been in Lubbock for training that included martial arts combat.

Summer Baldwin KCBD-TV

On Tuesday at 6 p.m., a day after his 38th birthday, Rodriguez is set for execution for the 2005 slaying of that woman, Summer Baldwin. She was 10 weeks pregnant.

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Court records show Rodriguez was linked to at least five other sexual assaults and confessed to the slaying of a 16-year-old Lubbock girl who had been missing for more than a year. Joanna Rogers' mummified remains were found, like Baldwin's, inside a suitcase at the city garbage dump. Rodriguez became known as Lubbock's "suitcase killer."

Lubbock County District Attorney Matt Powell, who prosecuted Rodriguez, described him Monday as "very cold-blooded and very calculated."

"What kind of person does that, just throws them out like the morning trash?" Powell said.

Rodriguez would be the fourth Texas inmate to be executed this year, and the seventh nationally.

Attorneys for Rodriguez appealed Monday to the U.S. Supreme Court as their "last hope" after lower courts rejected appeals that focused on the medical examiner who testified about Baldwin's autopsy at his trial.

Rodriguez's lawyers said the coroner recently settled a whistleblower lawsuit, previously unknown to them, that alleged he delegated some duties to unqualified underlings. The lawsuit "bears directly on the credibility and admissibility of the medical examiner's testimony in this case," attorney Seth Kretzer said.

Assistant Texas Attorney General Tomee Heining said Rodriguez's appeals were "nothing more than a last-ditch effort" that were improper, untimely and meritless. The settlement involving a dismissed former employee, who didn't start work until five years after Rodriguez went to trial, included a statement that there was no reason to question the scientific validity of findings or opinions made by the medical examiner's office. Court records show the medical examiner personally conducted Baldwin's autopsy.

Rodriguez was arrested at his parents' home in San Antonio days after Baldwin's body was discovered.

Court records describe Baldwin, the mother of four, as a prostitute. She'd served jail time in Lubbock for a drug conviction.

Three weeks after his arrest, Rodriguez gave Lubbock police a statement saying he killed Baldwin in self-defense when she pulled a knife on him after the two had consensual sex on Sept. 12, 2005, at a hotel room.

Testimony at his 2008 trial showed she had about 50 blunt force wounds and may have been alive when she was folded into the suitcase and tossed into a trash bin. The contents of the bin subsequently wound up at the city dump. Defense attorneys suggested a trash compactor could have killed her.

Jurors who convicted him of capital murder heard during the trial's punishment phase from five women, including his high school girlfriend, who testified he raped them. Jurors also heard about his confession to killing Rogers, the 16-year-old Lubbock girl who evidence showed he initially met in an online chat room.

Prosecutors decided to seek the death penalty after Rodriguez scuttled a deal where he'd plead guilty to killing Baldwin and the teenager in exchange for a life prison term.