The album is her first to be released independently. Sovereign once said, "I feel great now. I feel like I've overcome all my dark times. I get to pick who I want to work with. No one can tell me off or make me do things because I'm the boss. It feels amazing. I've got my own label and everything works my way." The album is Sovereign's reaction and reflection of her popularity and the inability to cope with it, up to the point where she had suicidal thoughts. About the album, she said, "The album is the next chapter. It's a massive leap forward for mankind." The album will also feature Sovereign singing; she explained, saying:
I was seeing someone, it was pretty deep. I was loved up. Then it all fucked up and I just wanted to sing about it really. I'm not the best singer in the world but you listen to it and you definitely feel it, you know. Rapping is second nature to me. I feel different when I sing. I feel lighter, it's fun.
She explained the album's title, saying it "makes sense to call the album Jigsaw because it's kind of like different genres".
Production and writing
The album includes production by Dr. Luke, Benny Blanco and Medasyn. Lady Sovereign said her first album was "not consistent", but "it worked" for her. On her new album, she went on to say, "A few of the tracks explain everything that's happened in the last two years, which I didn't get a chance to at the time." On production, she said she had been listening to electro and instrumental music. She stated that working with Medasyn is "an inspiration" because they "always come up with some weird beats together". Sovereign experimented with Auto-Tune in the album's lead single, "I Got You Dancing". The opening track "Let's Be Mates" is a club-oriented dance song, while "Student Union" is a 1980s synth-driven track. "Jigsaw", the title track, is a rapcore song supplemented by strings with a sung chorus.
Initial critical response to Jigsaw was mixed. At Metacritic, which assigns a normalised rating out of 100 to reviews from mainstream critics, the album has received an average score of 57, based on 25 reviews. ClashMusic.com commented that "Jigsaw" is "a record where standout offerings seem such because of the lack of a considered segueing between arrangements". But the review concluded that progression from "Public Warning" was evident, and that some listeners "will fall instantly in love with the cheeky wit on show, at turns charming and caustic".
