You Can Compare Them on Any Day : The Cranberries and Dolores O’Riordan are frequently likened to the Sundays and Sinead O’Connor. But the group’s singer doesn’t mind.

You’d think Dolores O’Riordan, the singer for the young Irish band the Cranberries, would be sorry she ever wrote a song called “Sunday” for the group’s debut album. She’s got to be sick of the word Sunday , because she is constantly compared to Harriet Wheeler, the singer of the English group the Sundays, which preceded the Cranberries down a path between “adult” pop and alternative rock.

Nope. In fact, O’Riordan says she wishes she’d also written a song with a title honoring the other artist she’s frequently compared to: Sinead O’Connor.

“If you call a song ‘Sunday’ or ‘Sinead O’Connor’ or something, it means that you don’t give a (expletive) what people say,” O’Riordan, 22, said in a voice as soft as her words are brash.

“It’s like I shaved my head as well on the last tour, a bit of an obvious one,” she continued during a recent phone interview. “I had it skinned. So I don’t really care about comparisons.”

Still, the comparisons, at least superficially, are themselves obvious. The Cranberries--who finish a two-night engagement tonight at the Palace, opening for Suede--combine the lush lilt of the Sundays with the vocal force and fire of O’Connor.

And like O’Connor, O’Riordan has an artistic personality that was indelibly imprinted by her Irish Catholic upbringing. But whereas O’Connor has rejected those roots, O’Riordan, who grew up and still lives in an isolated area near Limerick in southwestern Ireland, still embraces them.

“I played the church organ for about eight years and did a lot of Gregorian hymns and chants,” O’Riordan said. “Not a lot of young people do that anymore. Where I grew up there wasn’t even a town, but you had the church.”

Pop was pretty much peripheral in her world, which was dominated by traditional Irish, classical and church music, but she says that from early on, she had desires to explore the field.

“I always wanted to be in a band where I wrote songs, something creative and new,” she said. “I could easily do Irish trad for a living, but that wouldn’t make me happy because it was already there.”

The opportunity came four years ago when a schoolmate told her about a Limerick band that needed a new singer. O’Riordan went to see the act, then a novelty-oriented group with the punny name the Cranberry Saw Us.

O’Riordan signed on, and the group--which also includes guitarist Noel Hogan, bassist Mike Hogan and drummer Feargal Lawlor--was re-christened and began recording demo tapes to send to record companies. The result, O’Riordan says, was overwhelming for the small-town band.

“We had been together six months and had just six songs to our name, and 32 (record company) people flew in to see us and we were afraid for our lives,” she said. “I’d never even heard the term record company until I was 18. Then after we signed with Island in 1991, we got very hyped by the British press for six months.”

But the group held its focus, recording its debut album, “Everyone Else Is Doing It So Why Can’t We,” with Morrissey’s producer Stephen Street and gaining confidence in concert.

And now O’Riordan finds herself in a touted band on the road in America and getting favorable comparisons with the likes of O’Connor. All that has made her appreciate her isolated upbringing even more.

“I don’t want to be changed by all this,” she said. “It’s a hard thing to do, but keeping your head together is very important. We’re nothing yet, the Cranberries.”