Actor Johnny Depp's wife Amber Heard pleaded guilty on Monday to providing a false immigration document amid allegations she smuggled the couple's dogs to Australia, but managed to avoid jail time over what was dubbed the "war on terrier" debacle.

Prosecutors dropped two more serious charges that Heard illegally imported the Yorkshire terriers, Pistol and Boo, into the country last year, when Depp was filming the fifth movie in the Pirates of the Caribbean series. A conviction on the illegal importation counts could have sent the actress to prison for up to 10 years.

The false documents charge carries a maximum penalty of a year in jail and a fine of more than $7,650, but Magistrate Bernadette Callaghan sentenced Heard instead to a one-month good behavior bond. The condition means she will have to pay a $765 fine if she commits any offenses in Australia over the next month.

Depp and Heard said little to the waiting throng of reporters and fans outside the Southport Magistrates Court on Queensland state's Gold Coast, but did submit a videotaped apology to the court that was played during Monday's hearing.

"When you disrespect Australian law," a grim-looking Depp says in the video, "they will tell you firmly."

The drama over the dogs began last May, when Agriculture Minister Barnaby Joyce accused Depp of smuggling the tiny terriers aboard his private jet when he returned to Australia to resume filming the Pirates movie.

Quarantine regulations

Australia has strict quarantine regulations to prevent diseases such as rabies from spreading to its shores. Bringing pets into the country involves applying for a permit and quarantine on arrival of at least 10 days.

"If we start letting movie stars - even though they've been the sexiest man alive twice - to come into our nation (with pets), then why don't we just break the laws for everybody?" Joyce said at the time. "It's time that Pistol and Boo buggered off back to the United States."

Depp and Heard were given 72 hours to send Pistol and Boo back to the US, with officials warning that the dogs would otherwise be euthanized. The pooches boarded a flight home just hours before the deadline ran out.

The comments by Joyce, who is now the deputy prime minister of Australia, elevated what might otherwise have been a local spat into a global delight for comedians and broadcasters. One newspaper ran a doggy death countdown ticker on its website that marked the hours remaining before the dogs had to flee the country, and comedian John Oliver dedicated a more than 6-minute segment to lampooning the ordeal.