Tyler said he was largely satisfied with the amendments. His lawyer, Dina LaPolt, agreed immediately after the hearing but said she planned to go over the changes more fully.
English says the bill is necessary to protect privacy in the digital age.
He says that while the constitution protects news publishing, it doesn't protect news gathering.
Stirling Morita, president of the Hawaii chapter of the Society of Professional Journalists, said he disagrees.
He says even with the bill's amendments, it's still too vague.
"You have to be pretty definite to limit First Amendment rights," Morita said.
The bill was also opposed by the National Press Photographers Association, which submitted testimony on behalf of the Society of Professional Journalists, the Associated Press Media Editors and the American Society of News Editors, among other media groups.
More than two-thirds of the state Senate co-sponsored the measure. Britney Spears and Avril Lavigne were among more than a dozen celebrities who submitted testimony supporting the bill along with the rockers.
The stars say paparazzi have made simple activities like cooking with family and sunbathing elusive luxuries and the bill would give them peace of mind.
Tyler said stars today are pestered much worse than previous generations given modern technology and lucrative paydays for paparazzi.
The unusual hearing packed a conference room in the Hawaii Capitol, and generated buzz from state staffers who captured cellphone pictures of Tyler and Fleetwood, then compared snapshots in the hallways after the hearing.
Cameras clicked excitedly when the musicians walked into a room packed with lawmakers, staffers, media and other onlookers.
Sam Slom, the sole Republican in Hawaii's 25-member Senate, ribbed Tyler about tabloid magazine photos that showed the singer in a revealing bathing suit.
"Mr. Tyler, it's a pleasure to see you in clothes today," Slom said.
Anita Hofschneider can be reached at http://twitter.com/ahofschneider
Text of bill: http://1.usa.gov/YfbJqi