Adapted from wiki:-

Jesse Garon and the Desperadoes were a Scottish band formed from around, and within, the Edinburgh indie pop scene of the mid-1980s. The band had a distinctive guitar-jangle sound with male and female vocals. The band took their name from Elvis Presley’s stillborn twin brother, Jesse Garon Presley.

The original members of the band were Andrew Tully (guitars/vocals), Angus McPake (bass guitar), Fran Schoppler (vocals), Margarita Vasquez-Ponte (drums), Kevin McMahon (guitars), and Stuart Clarke (guitar). Tully, Webster and Vasquez-Ponte were also members of Rote Kapelle, a band that was active from 1985–1988.

This initial line-up recorded the first two singles, “Splashing Along” and “The Rain Fell Down” on Narodnik Records. With the departure of McMahon and Clarke, Bruce Hopkins and John Robb were drafted in for third single, the Billy the Whizz EP; these being replaced on a more permanent basis by Michael Kerr (of Meat Whiplash).

Next release was a flexi-disc featuring the track “Hank Williams Is Dead” along with a track by The Fizzbombs, a side-project of Margarita and Angus, along with Ann Donald of The Shop Assistants. Moving to Velocity Records, the band released two more well-received singles, “The Adam Faith Experience” and “You’ll Never Be That Young Again”, followed by first album, A Cabinet of Curiosities, which collected the tracks released to date.

In 1989, Michael Kerr left to join The Darling Buds, and the rest of the band returned in 1990 with single “Grand Hotel “, a reference to the IRA bombing of Brighton’s Grand Hotel, the venue for the Conservative Party conference. Andrew Tully described this as a “fuck Thatcher and fuck the IRA for not killing her when they had the chance” song. The album Nixon followed, and in October 1990, they released their final single, the Hold Me Now EP.

Here’e the rather wonderful jangly debut 45 (which makes a few references to my home city):-

mp3 : Jesse Garon & The Desperadoes – Splashing Along

And here’s a later 45 with the slightly different line-up:-

mp3 : Jesse Garon & The Desperadoes – The Adam Faith Experience

The latter offers up a more polished track (relatively speaking!!), but I’m more fond of the debut.