If any band in the world was predestined for musical success, it was California residents That Dog. Lead singer Anna Waronker was the daughter of the then-president of Warner Brothers’ A&R (now president of Dreamworks), Lenny Waronker. Her grandfather Si Waronker was a well-known record-label owner and producer.

Adding to That Dog’s lineage, fellow members Rachel and Petra Haden are the offspring of jazz bassist Charlie Haden. Drummer Tony Maxwell’s father is hypertension expert to the stars.

On the surface, it seems that a few phone calls could solve any recording dilemma in short order, but that was not the case. Warner Brothers never called.

Then again, That Dog’s self-titled debut album didn’t sound like a corporate hand had anything to do with it. Waronker sang and played guitar, Maxwell kept the kit, Rachel Haden played bass, and Petra played violin. While this setup could be construed as a game of “one of these things is not like the others” gone awry, it wasn’t.

That Dog caught a different type of pop. Released in 1993, the record had its share of distorted, shambling rock, but coupled that sound with gorgeous vocal harmonies and a violin. The resulting mix was something like a female version of Pavement — with a violin.

The album did well on college campuses and received minor press attention, but was more or less ignored by the general public.

However, people paid just enough attention for That Dog to snag a space opening for artists like Mazzy Star and even Johnny Cash. It was the group’s spot as Beck’s opener on both his European and American tours that really got the band noticed.

Boosted by the success of Beck’s “Loser” single, That Dog got a better promotional deal for its second disc, Totally Crushed Out. Most critics quickly wrote off the album as sub-par, but it did have its high points. Songs like the single, “He’s Kissing Christian,” stretched newfound legs and hinted at things to come.

Better described as a transitional album, Totally Crushed Out finds itself midway between two completely different bands — one disorganized rebellious noise, the other polished pop execution. Totally Crushed Out is sometimes hit-or-miss with its efforts to satisfy both demons, but definitely hints at a new direction.

That Dog didn’t achieve full pop-star status until 1996’s Retreat From the Sun. Produced under the diligent eye of Brad Wood (Liz Phair, Sunny Day Real Estate, Veruca Salt), Retreat abandoned discord in favor of beautiful melodies and more personal lyrics.

That Dog essentially produced its first two albums, only working with engineers, but the addition of a dedicated professional in the producer position freed the band to concentrate on the basic material. If the previous dogma with recording was “What can we do live?” then the new one was “What does it need?”

As always, the album’s harmonies are beautiful. The Haden sisters’ voices both match each other and accommodate Woronker’s vocals so well that listeners often feel as if they are drowning in voices. Waronker herself has a buttery voice with a rich midrange to melt even the most discerning ears.

Petra’s violin makes appearances on several tracks, but this time it is complimented not only by guitar, bass, and drums, but also by a retinue of equipment from piano to French horn to the castanets.

Lyrically, Waronker provides more disclosure and more sensitive topics. Originally, the material ultimately used for Retreat was intended for Waronker’s already anticipated solo career.

Far from the bubblegum content of the band’s first two albums, songs like “Gagged and Tied” and “I’m Gonna See You” took on more mature themes. “Gagged and Tied” follows its protagonist’s desire to subjugate and dominate the object of her affection despite the situation’s irrationality: “Mistress never tells a lie / Would you love me gagged and tied / It’s not your style, I can see you crack a smile.”

“I’m Gonna See You” is all about not getting tied down in marriage. Sarcastically optimistic lyrics like, “We’ll have wedding dreams / and baby seats / and family gatherings / eternally, you and me,” set the song’s tone.

In the album’s single, “Never Say Never,” Waronker penned an infectious keyboard line full of glissando. The song hits hard from the start, erupting in a cacophony of fuzzy distortion, then relaxing into an easy gait.

Likewise, “Minneapolis” pushes the tempo and a simple guitar riff to catch the listener while Waronker plays with different pronunciations of the city’s name. “Long Island” starts out with the shout, “You’re pretty dreamy for a guy from Long Island,” then rushes headlong into itself.

While That Dog toured in support and received attention for Retreat From the Sun from publications as large as Spin, CMJ and Rolling Stone, it never managed to achieve classic standing based on numbers alone.

Finally, the band decided to part ways for brighter beginnings.

A reunion looks more and more unlikely as the years go by. Waronker has devoted herself to her solo recordings and released an album titled simply “Anna” in late 2002. She also runs Five Foot Two Records.

And while Tony Maxwell’s accomplishments in recent years are too many to list, it bears noting that he not only co-wrote the music to “The Good Girl” but also choreographed all of the dance scenes in “Being John Malkovich.”

That Dog, named after California roadkill, may never have made it all the way to the other side of the road, but it certainly didn’t end up on their back in the median. Used-bin aficionados know the band’s name and remember it when they need to retreat from the sunshine of insincerity and heavy-handedness the record industry serves up with almost carcinogenic frequency.

Information and tracks can be found in the links section of www.annawaronker.com.