The 1980s saw a host of influential bands from Britain, but most people on this side of the Atlantic probably never heard of them. Groups such as the Smiths and Jesus and Mary Chain shook up the bland world of ’80s new wave and pop with new ideas, styles and sounds. Another group with the same fate was the Scottish band Cocteau Twins.

Now, American listeners can get a good look at this underrated band’s beautiful music with its latest release, The BBC Sessions (Rykodisc).

The two-disc set album contains songs the band recorded for the BBC in the early 1980s. The Cocteau Twins was one of the first bands to come under the dream-pop label. Never was a characterization more accurate.

The band’s dark, melancholy sounds, laden with fuzzy guitars and synth effects, made for a haunting listen that often sounds like the audio equivalent of a dream – something that floats on the edge of memory but that you can’t quite grasp. Add to that a beautiful female voice singing lyrics that you could only pick out one or two words of. This m?lange of sounds defines the band’s label, 4AD, and led to the early 1990s trend of shoegazing, which a host of other bands emulated. The trend is named shoegazing because the band members would stare at their feet as they played.

The album opens with a series of songs taken from the band’s first few albums in 1982 and 1983. Songs such as Wax and Wane and Garlands combine the synth-pop sound popular in the early ’80s with the darker sound of the burgeoning Gothic scene of the time. However, the Cocteau Twins was able to wisely avoid being pegged as a Goth band by lacking the mopiness associated with many of those bands.

Instead, the songs had an ethereal quality to them. Unlike many 1980s albums that sounded great at the time but now sound dated, the music on The BBC Sessions sounds contemporary and in many ways ahead of its time. The reason – the band was making music in the early ’80s that was out of step with the prevailing styles of new wave and synth-pop.

One unexpected cover on the first disc is a remake of Billie Holiday’s seminal Strange Fruit. It’s hard to imagine anyone tackling such a legendary song, much less do justice to it. However, the Cocteau Twins pull it off. Emphasizing the music over the vocal, the band creates a dark and sinister atmosphere that fits the song perfectly. Although you can’t hear the story about a lynching and bodies of African Americans hanging in trees as victims of racial violence, the music gets across the same feelings without relying on words.

The second disc isn’t as good as the first, a problem common with many two-disc sets, but it still has its moments. The first three songs – Hitherto, From the Flagstones and Musette and Drums – are taken from an appearance the band made on Saturday Night Live in 1983. It’s hard to imagine this kind of band on SNL. The other songs that follow lean more to the dream side of dream-pop, and lack the hooks and atmosphere of the songs on the first disc.

Another minor flaw of the set is that it draws mainly on the band’s early works, leaving much of the band’s long career underrepresented. There also are repeats of songs taken from different radio shows where the band performed. The difference between the versions isn’t enough to justify the repeats. And lastly, diehard fans looking to see what the Cocteau Twins sound like live will be disappointed, because these songs often sound like the studio versions.

But these are all minor flaws. Ultimately, The BBC Sessions is a great way to get acquainted with a relatively unknown band. While the Cocteau Twins never achieved mainstream success, this album shows that creating beautiful music that has a huge influence is often better.