Story highlights An appeals court invalidates two of Casey Anthony's convictions, upholds two others

She was convicted of four counts of lying to authorities during an investigation

The investigation was into the disappearance of Anthony's 2-year-old daughter, Caylee

Anthony's attorney said his client wants to "keep fighting" after hearing about ruling

One of the most infamous defendants in U.S. trials of recent years took two big steps Friday toward clearing her name, and she vowed to "keep fighting."

Florida's 5th District Court of Appeal threw out two of Casey Anthony's four convictions of lying to authorities as they investigated the disappearance of Anthony's 2-year-old daughter, Caylee.

The appeals judges agreed with Anthony's argument that the multiple convictions amounted to double jeopardy. But the judges upheld the other two convictions.

In an internationally publicized and emotionally charged case, Anthony was tried in 2011 and acquitted of murder charges in the death of Caylee.

The child was last seen June 16, 2008, but was not reported missing until July 15, 2008, when Casey Anthony's mother tracked her daughter down and demanded answers regarding Caylee's whereabouts. Investigators searched for the child for five months, eventually finding Caylee's skeletal remains in woods less than a mile from her grandparents' Orlando home.

While she was acquitted in the death of her young daughter, Anthony was convicted of the four counts of lying to authorities. Those charges arose from statements Anthony made on July 16, 2008, to Orange County Detective Yuri Melich, who was investigating the disappearance of Caylee.

According to Friday's court filing, the appeals judges rejected Anthony's claim that statements she made before being read her Miranda rights should not have been allowed in the trial. And they rejected her argument that the state statute she was convicted of violating is unconstitutionally vague.

Anthony's lawyer, Cheney Mason, said when he called his client to share the ruling that two of the four convictions had been overturned, she said, "We keep fighting."

Anthony could appeal the remaining two convictions to the Florida Supreme Court next.

When questioned early in the investigation, Casey Anthony admitted to police that she hadn't seen Caylee for more than 30 days, and on July 16, 2008, she was arrested on suspicion of child neglect, filing false official statements and obstructing a criminal investigation. At that time, she made the statements to Melich, which led to her convictions.

After nearly three years of legal maneuvers, Anthony's capital murder trial began on May 24, 2011.

Prosecutors alleged that she killed Caylee by using chloroform and covering her nose and mouth with duct tape, and that she put her body in the trunk of her car before dumping it in the woods.

Defense attorney Jose Baez argued that Caylee drowned in the Anthony family pool on June 16, 2008, and that Casey Anthony and her father, George, covered up the death.

On July 5, 2011, a jury found Anthony not guilty of first-degree murder, aggravated child abuse and aggravated manslaughter of a child, while convicting her on the four "false information" counts.

Anthony was sentenced to four years in jail, to be served consecutively. But with her time in jail as she awaited trial counting against the jail terms, she was released 10 days after her sentencing, on July 17. Even though she exited shortly after midnight, about 1,000 people jeered her as police guards and Baez escorted her to a waiting SUV and drove away quickly.

Anthony still faces a defamation lawsuit from Zenaida Fernandez-Gonzalez, of nearby Kissimmee, Florida.

During Anthony's disputed July 16, 2008, statements to Melich, she said the last time she had seen her daughter was when she dropped Caylee off at Gonzalez's apartment.

Gonzalez filed suit in September 2008, claiming that Anthony ruined her reputation.

Last April, a judge ruled that the suit needed to go to trial by jury and denied Gonzalez's request for a summary judgment.