It seems Amy Winehouse is a prominent person — she apparently has been granted the nonimmigrant visa speedily.

Christian Slater

Christian Slater was sentenced to serve ninety days in December 1997 for his August 1997 battery on a dating partner, battery on a peace officer, and being under the influence of a controlled substance. Battery of a dating partner is deemed a crime of domestic violence by immigration judges in California. The crime is a deportable offense. INA § 237(a)(2)(E). Being under the influence of a controlled substance is also a deportable offense, INA § 237(a)(2)(B)(i), as is being a drug abuser or addict. INA § 237(a)(2)(B)(ii). As he was sentenced to less than a year for the crimes of violence, he is not an aggravated felon and would be eligible for Cancellation of Removal relief, INA § 240A(a), for these crimes.
Earlier, in 1994, Mr. Slater pled guilty of a possession of an unloaded pistol. At the time, this crime would have rendered him deportable and ineligible for a pardon pursuant to the pardon statute at that time, INA § 212(c). Because of a quirk in the law, he might have been able to avoid deportation if he had a United States citizen wife. This crime is currently pardonable under the Cancellation of Removal form of relief. Had Mr. Slater been placed in removal proceedings and received Cancellation of Removal for the weapon charge before December 1997 and then gotten placed in removal proceedings again, he could not ask for this relief a second time for the domestic violence conviction and would be deported. INA § 240A(c)(6).

Kelsey Grammar

Kelsey Grammar pled guilty to cocaine possession in 1988. The controlled substance violation would have rendered him deportable, INA § 237(a)(2)(B)(i), but he would have been eligible for a pardon under Cancellation of Removal.

Randy Duke Cunningham

Randy Duke Cunningham resigned from the House of Representatives (California’s Fighting 50th District) on November 28, 2005, after pleading guilty to accepting at least $2.4 million in bribes and underreporting his income for 2004. He pled guilty to federal charges of conspiracy to commit bribery, mail fraud, wire fraud, and tax evasion. On March 3, 2006, he received a sentence of eight years and four months in prison and an order to pay $1.8 million in restitution. The convictions render him an aggravated felon, INA § 101(a)(43)(M), and ineligible for any waiver of deportation.