Following various false starts and stints on backup for the likes of Rufus Wainwright and Antony Hegarty, Joan Wasser's debut album under the Police Woman guise was released when she was 35 years old, and already sounded like the work of someone who had dealt with unaccountable tragedy and loss. 2006's Real Life was – and remains – a revelation of an LP, and if it's one that she has never topped in terms of sheer impact and durability that's only because she set the bar so high on her first attempt.

"I'm in the best place I've ever been in my life," Wasser declares in the press release for The Classic, the group's fourth album of original songs. It's a sentiment borne out in its title track, which is simultaneously a high point and something of an island here. Against a backdrop of doo-wop gospel and a cappella beats 'n bass (the latter provided by comedian Reggie Watts and singer Joseph Arthur respectively), the song is a giddy paean to love, joy and comfort: "I love how it feels to be so high, without sinning," Wasser exults. "Could it be that you, you are the one?" the choir chime in. It doesn't so much skirt cliché as deliriously embrace it, and the result is irresistible.

Elsewhere Wasser and her players work off the template that 2011's bigger, broader The Deep Field established. The results are mixed: these are fine songs - sometimes fierce, always compassionate, and all elevated by Wasser's delivery and an assured group of players. Yet, embellished by all manner of strings, brass and backing vocals, they come across busy and overcrowded (something the sparse title track unfortunately throws into focus).  'Holy City', a song inspired by a visit to Jerusalem's Wailing Wall that extolls and advocates freedom of expression, is a case in point. Its urgent, loping rhythm is reinforced by blares of trumpet and squalling electric guitar, punctuated by panting and harmonic backing vocals, before its closing third is given over entirely to Reggie Watts' scat-rapping. It is overlong and overstuffed to the point where it squanders your attention - a shame, as there's a great song in there, amid the bombast.

The problem isn't that Wasser can't front these bold, ambitious arrangements - bravura finale to The Deep Field 'I Was Everyone' and various other songs from her discography make it abundantly clear that she can - it's just that she ought to do so a little more sparingly. As such, what could be throwaway moments from songs like the subdued and effortlessly sensual 'Get Direct' resonate with far greater impact than the everything-and-the-kitchen sink mentality of the entire 'Good Together'. (The way she squeezes all she can out the word "business" in the line "The corner of my eye, it's got some business with you," for example, is a treat.)

The forthright 'What Would You Do' collapses into a moving coda to finish, and its themes of empowerment and courage in the face of hardship (themes Wasser returns to time and again) are all the stronger for it, while the subtle textures and reverb of 'New Year's Day' are a genuine pleasure. The closing 'Ask Me' flips the script on much of the rest of the record, too. Trading powerhouse soul for a twinkling, reggae-infused rhythm that forms the backdrop to a tentative acceptance of proffered love, Wasser equates beauty with arousal by way of the mundane to illuminate the kind of wondrous fear that comes with truly letting someone else into your life.

The Classic is a flawed piece of work, no doubt; overly cluttered and in sore need of reining in at times, it suffers for the hubris of its title. But when Wasser hits the sweet spot, as she does on 'Ask Me', 'Get Direct' and its ebullient centrepiece, she hits it with conviction. "Let's keep it going," are the words that ring out as the record finishes. In the context of the song it isn't entirely clear whether they should be interpreted as a question or a statement, but in the light of what she and her Police Woman outfit can conjure up at their best, it would be wise indeed to hope for the latter.