They've been through their fare share of drama over the last few months, losing original member Keisha and rumours of Amelle being kidnapped. Thankfully the trio, which now includes Jade Ewen, are still around to explain it all.
It's a girl band that's seen four different line-ups in 12 years, and now contains none of its original members, still the same group?
As you might imagine, the Sugababes are emphatic with their answer.
"We never thought for a second that we should change our name," says Amelle Berrabah, who became a Sugababe after original member Mutya Buena's departure in 2005.
"It honestly never crossed my mind. When I think of original members, I always see Heidi [Range] as one anyway, she's been in the band eight years now."
"I was in the band with Mutya for four years, and Amelle has been in the band four-and-a-half," says Heidi, who joined the band when Siobhan Donaghy 'went to the toilet and never came back' while on tour in Japan in 2001.
The latest drama in the Sugababes's story began back in September. Rumours arose that Amelle had left the band, citing working difficulties and exhaustion as the reasons. Newspapers then ran stories claiming she hadn't been seen for days and was presumed kidnapped.
Of course, this wasn't true.
"That story made me laugh so much," Amelle says. "I just did one and turned my phone off," she says.
Former Eurovision contestant Jade Ewen was then mooted as a possible replacement for Amelle and the show would go on. Within days of an announcement about Amelle leaving, however, another followed saying it was in fact founding member Keisha Buchannan who was leaving the band apparently due to her bullying.
Using her Twitter page to defend herself, Keisha stated no bullying had taken place, and her leaving was the result of a "break down in communications".
Speaking to Heidi and Amelle, it sounds a little more serious than that.
"For a good year, me and Heidi weren't happy and it just got harder and harder," explains Amelle. "And it wasn't just us, there are other people that we see every day that were finding it difficult too."
Throughout the conversation, they never explicitly say what Keisha used to do that was so bad, although there are hints at dramatic mood swings, difficult, obstinate behaviour and deliberately being late to make things difficult for others involved.
As things came to head, both Heidi and Amelle decided enough was enough and quit the band.
"Keisha wasn't kicked out," says Heidi, defensively. "We left, and while we were waiting to find out whether we'd still got jobs - we didn't know what the label were going to do, get two new girls in or whatever - people we worked with told us they were about to leave as well because they couldn't cope with the situation either."
"We weren't happy, but it was a massive decision to leave, it was a massive risk," adds Amelle. "We love what we do, but it got to the point where it had to change."
"Life's too short to go through it, to live through that on a daily basis," concludes Heidi, sagely. "No one would go to work like that."
If kidnap plots and ever-changing members weren't dramatic enough, they're nothing compared to what happened in the aftermath of Keisha's departure.
As she left, the girls were due to fly out to America to film a video. A band member down and their future in doubt, Heidi and Amelle could do nothing but sit tight in an LA hotel and weigh up their options.
Meanwhile, back in London, Sugababes's management company, Crown, were busy trying to find a replacement.
That's where Jade Ewen comes in. Before Crown Management came knocking, Jade was trying to get her solo career going. As she admits herself, it was proving difficult, with the dreaded Eurovision Song Contest acting like a weight around her neck.
"If it wasn't for Eurovision, no one would know who I was," says Jade, candidly. "But at the same time, I couldn't get in magazines or on the radio because of Eurovision, so it was a double-edged sword really."
Fortunately for her, Team Sugababes saw past that - she did come fifth in 2009, after all, the highest British placing for seven years - and invited her to join the band.
"At first I'd said there was no way I wanted to be in a band, because I'd been in a girl band before where I was the youngest of three girls, it was such hard work and we didn't get anywhere," says Jade.
"I woke up one morning to someone shouting through my letterbox saying 'Pack your bags love, we've got to go'.
"Management said 'I know it's on the spot, but if you want to be in Sugababes, the girls are out in LA now and they were supposed to have shot the video yesterday. They're out there, but there's no band'. So I said yes, without really knowing what to expect - at that point I didn't even know who I was replacing, as far as I knew Amelle was still missing."
There then followed a tentative meeting where the girls were introduced to see if they'd get on. Heidi and Amelle insist they thought Jade was right from that initial chat, but feared she might get cold feet.
"Our manager had a chat with Jade on her own after we'd all met," says Amelle. "Heidi and I were hoping that if she didn't want to join, she'd say then and could just leave quietly."
"I said 'She'll either be here in half an hour, or on the plane home'," says Heidi.
Two quick rehearsals later and Jade had filmed a video as part of Sugababes, and shortly afterwards went on holiday to Barbados with her two new friends.
"We have all got so close these last few months especially, and we have lots of fun," says Amelle.
"We're all just so much happier."
Extra time - Sugababes :: Sugababes have released 25 singles since 1998, six of which have reached No 1.
:: Before joining the band, Jade's favourite Sugababes songs were Too Lost In You and Freak Like Me.
:: Prior to Eurovision, Jade had featured in girl band Trinity Stone.
:: Sweet 7, the band's seventh album, was finished last year and featured Keisha's vocals. They have now been removed and Jade has re-recorded all her vocal parts.
:: In January, Heidi announced her engagement to TV and radio presenter Dave Berry.
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