There used to be stories told, with an understandable air of reverence, about great jazz musicians who could sketch out big band arrangements on a cigarette packet while sitting amid the hubbub of the band bus.

Well, the National Jazz Institute of Scotland doesn't run to band bus simulators - nor does it encourage smoking, but there's every chance that by the end of the Institute's third-year course, such a feat will be second nature to its students.

Opened on Strathclyde University's Jordanhill campus in autumn 1995 to fill a gap in formal jazz education in the national curriculum, the Institute is already achieving results and international recognition.

Director of music, saxophonist Tommy Smith, reports that some of the work the course's sixty-odd students are producing on their assignments is ''fantastic''.

The Institute not only attracts students from Scotland but from Germany, too, and last year gave out its first scholarship - to a Brazilian bassist Mario Caribe, who saw an ad for the Institute while on holiday in Glasgow during the jazz festival. He applied, was accepted, moved his family to Glasgow while he studies, and is currently gigging as well as holding down the bass chair in Smith's Beasts of Scotland sextet.

Scholarships are not given out lightly either - the Institute still needs all the student fees it can get, so Caribe is an exceptional case. His is also an example to budding students. ''They have to do the work, and it's hard,'' says Smith. ''But we can see great improvements even after the first year.

''We have students studying most instruments and at various standards of ability from 15 to 35, and they get a real grounding in jazz. Twelve credits, which means passing all subjects in the first two years, gives them a certificate of Higher Education in Jazz.''

The classes run from 10.15am to 5pm for 24 Saturdays from October to May.

A typical day breaks down thus: mornings cover jazz history, ear training - a very important part of the curriculum which Smith feels is neglected in schools, and theory; afternoons highlight music technology, piano study, and ensemble playing (the budget doesn't as yet run to individual tuition).

First-year students learn the history of jazz, from its origins in Africa through New Orleans, the Swing era, bebop, cool jazz, modern jazz, hard bop, up to jazz/rock. Each of these categories is examined in depth with lots of listening involved, and at mid-term the students compile a 2000-word essay on a musician of their choice.

''Very often students come in who only have two or three albums,'' says Smith. ''But here we have access to Jim Waugh's (the late jazz broadcaster) record collection and they can tape tracks and expand their collection that way.''

The route to better musicianship gets seriously under way in year two when, as Smith says, ''we really go to town on harmony.'' Standard songs are rearranged, initially for four horns, and the arrangements played in class. ''Getting to hear their work is a big moment,'' says Smith, ''and when we move on through various styles and line-ups to big band, the best arrangements get played by the Scottish National Jazz Orchestra, which gives the students a terrific buzz.''

As well as harmony studies, famous solos such as Miles Davis's trumpet feature on So What? are dissected so that students can decide how to approach their own solos.

Year three's major subject is composition. By the end of their third year Smith hopes to see all students with small portfolios of their own compositions. ''We want to bring out their creativity and individuality rather than just produce clones, and composition is an important factor in these things alongside the sound they make and the improvisational ideas.''

Sound and ideas are taken into consideration along with musicality and sight-reading ability from the beginning when Smith and Bobby Wishart, musical director of Strathclyde Youth Jazz Orchestra, carry out auditions for new entries in August. Joining them as tutors are guitarist Laurie Hamilton, pianist David Milligan, and music technology specialist Ian Massey.

The Institute also has executives in John Dankworth and vibraphonist Gary Burton, previously Dean of Curriculum and currently vice-president at Berklee School of Music in Boston, whose advice has been invaluable. Smith also hopes to have further seminars along

the lines of those given by visiting musicians.

''We have good resources now, having bought equipment with the help of the Scottish Arts Council lottery funding as well as building up a library of music and recordings,'' says Smith. ''And as well as providing performing opportunities for musicians, what we're aiming for is to establish year three, to set up an annual conference on jazz education so that we can exchange ideas with other organisations, and to really establish Bobby Wishart's outreach project. That's been a great success, going out to schools and community centres all over the country, helping teachers get started teaching jazz in schools.''

As for the Institute's own students, ''they love it,'' says Smith. For further information and an application form, telephone or fax 0141 950 3543.