Glance at the names in bold type and you will spot a theme to this week's column: young, female singer-songwriters with attitude. The youngest of them all, and, let's face it, the youngest person in the world, is Alanis Morissette. In October she was at the same venue, the Shepherd's Bush Empire, doing the same set, with the same band, and looking, roughly, the same. Six months later, she still has the widest smile and the longest hair in showbiz.

Her energetic performance still centres on that stomping, stooped dance, as if she's weighed down by the mass of her tresses. Her harmonica playing is still designed to make those of us who can manage only the opening bars of "Love Me Do" feel better about our abilities. And she is still an extraordinary talent. But, since October, everything's changed. She's won a Brit, and the hearts of the Brits. Her album, Jagged Little Pill (WEA), is in the Top Five, and "Hand in my Pocket" has become an anthem. On Monday, as she yodelled, "I got one hand in my pocket / And the other one is giving a peace sign", the fans made the predictable gestures without a blush among them.

One weird Morissette fact is that she looks just like Dave Grohl, formerly the drummer of Nirvana; and her drummer looks just like Nirvana's singer, Kurt Cobain. Unfortunately, her band think they really are Nirvana, with a slab of Metallica thrown in. They bashed sweatily at her askew, corrugated songs, until each one was hammered flat; then they scrawled all over them with Meat Loaf-ish guitar solos. It's a relief that her closing number, a new break-up ballad, was played on acoustic guitar. Breaking up is hard to do, but it's time to write the boys in the band their "Dear John" letters.

On Wednesday, at the Empire again, Aimee Mann introduced herself as Alanis Morissette. However ironic she intended the remark to be, there are similarities. Both are partial to ironic remarks, both write songs full of defiance, bitterness, intelligence and swear words. A closer analogy, though, would be to say that Mann is a pale imitation of Chrissie Hynde. Not a poor imitation, just frighteningly pale. Mann seems to be almost albino. Otherwise, she is a pretend Pretender. She is as skinny as Hynde and she has the brassy, nasal, quavering, high voice off pat.

What her vocals don't quite have is the emotional expression of Hynde's, not tonight anyway. Instead, the ironic tone is taken to the point of aloofness, as if she's looking down at her own songs. And, as on her latest album, I'm With Stupid (Geffen), her new-found, lo-fi minimalism doesn't serve her as well as she would like. It's attractively unusual when she swaps bass for acoustic guitar, and her guitarists switch to accordion and melodica. On a song like "Fifty Years After the Fair", it's spell- binding. Elsewhere, though, it adds to the impression of a slightly undernourished, undernourishing show. Seventy minutes may be a perfectly respectable length of set, but don't try to disguise it by stopping after 50 minutes, then returning for three pre-planned encores.

Considering that Natalie Merchant looks like Alanis Morissette wearing one of Bjork's dresses, you might expect her to be up there with Rik Mayall in the lunatic extrovert stakes. But the former leader of 10,000 Maniacs, now touting her debut solo album, Tigerlily (East West), opened her show at, yes, the Empire, as a shrinking violet. In the shy awkwardness stakes, she is up there with ... well, her band, a geeky ensemble who could be the school Dungeons & Dragons club. There are not many gigs where the bassist spends the evening hiding in the wings.

But one by one, different parts of Merchant's body started dancing. First her arms snaked into a gentle backstroke. Her hips began to gyrate, her mane of glossy hair swished, and finally she took off her clumpy shoes, and her legs joined in. She seemed less like one woman dancing than a crowd of independent body parts that happened to be having a party on the same skeleton. The band gave a similar impression, that of a group of musicians making it up as they went along, not really hearing each other, but loosening up and jamming until they'd worked themselves into a flurry of Latin-spiced sound. Three quarters of an hour after coming on-stage, Merchant wished us good evening, and the show got underway.

You can, of course, get too loose. A concert is perhaps not the time to teach your organist a song from scratch, nor is it necessarily a good idea to cover a song if you know only one verse. On the other hand, it was the casual warmth of this rambling shambles that the audience seemed to love, and, hearing Merchant's astonishing, country singer's voice, it would be churlish to blame them.

Moving on from the American- Women-At-The-Shepherd's-Bush-Empire segment of the column, we come to Tasmin Archer, who hails from Bradford, and who was at the Bloomsbury Theatre on Tuesday. This was a welcome change, and, more than that, the decision to perform in a small, stiff, all-seated auditorium was a signpost pointing in the direction her career has turned. Her first album, Great Expectations, had a completely appropriate title. Less so its follow-up, Bloom (EMI). It contains some very fine songwriting - she has more in common with Elvis Costello than her use of the Attractions' rhythm section - and the late-Beatles arrangements are well done. Her voice is luxurious and creamy smooth, particularly in the lower register. She'd sing an excellent Bond theme. But she seems to be restricting herself to an audience of Gradpop fans: a clique of discerning adults who will sit quietly in the theatre and appreciate her show rather than enjoy it.

If Merchant's musicians are the class geeks, Archer's are the geography teachers. Their backing is as professionally modest and unassuming as their dress sense. There was also a literal gap that widened the metaphorical one between the audience and the band: they were barricaded behind monitors at the back of the stage. Seeing them, the unresponsive audience and the empty seats dotted around the theatre, then seeing Archer, in her glittery eye-shadow, and a baggy dress that was crumpled into folds as if she had shrunk a few sizes since putting it on, was a bit embarrassing. She seems like the only one to have turned up to the party in fancy dress. Still, at the end of a week of four concerts, it's Archer's tunes - the swaying choruses of "Sweet Little Truth" and "One More Good Night With the Boys" - that are orbiting round my head.