Council housing bosses today confirmed homelessness applications in the city have dropped almost a third in the last decade.
The numbers were still falling in 2011-12 as post-devolution policies aimed at eradicating unintentional homelessness clicked into place.
However, experts are still worried.
Independent research carried out for housing charity Crisis suggests homelessness will begin to rise again because of welfare policies adopted by the UK Government and a shortage of homes for cheap rent in Scotland.
Professor Suzanne Fitzpatrick, of Heriot-Watt University in Edinburgh, who led the Crisis research, said: "Encouraging recent trends, strongly associated with targeted policy measures in Scotland, could be in jeopardy.
"It remains to be seen whether such gains can be maintained in the face of the prolonged recession, radical welfare cutbacks, and a tightening supply of affordable housing for those on low and modest incomes."
Figures for Glasgow and Scotland remain positive, especially compared to rising homelessness in England and Wales.
l In 2001/02 there were 13,244 homelessness applications in Glasgow.
l In the last full financial year, 2011/12, there were 9144 applications. That is a drop of 31%.
l Crucially, the figure for 2011-12 was 12% lower than the year before.
l Homelessness is falling even faster across the rest of Scotland, by almost a fifth in 2011-12 alone, to 45,322.
Experts such as Professor Fitzpatrick believe the fall is down to "pro-active" policies by councils such as Glasgow, although she admits recording practices may also have nudged the numbers down.
The Scottish Government has strengthened the statutory safety net for people facing homelessness.
Starting soon, all unintentionally homeless people will be entitled to be housed. This, unlike in England, includes all single people.
Glasgow, meanwhile, has overhauled its homelessness policies in recent years, closing big faceless hostels.
In the past many people would declare themselves homeless several times a year as they drifted from one hostel to another, from one living-room couch to another.
Sources believe the new system – where people are encouraged into emergency furnished accommodation rather than what could be fairly chaotic hostels – has reduced the number of "repeat customers".
A council spokesman said: "The overall trend for homelessness in Glasgow is downwards.
"This fits with the general national trend and in the last year alone applications in Glasgow have gone down 12%.
"Glasgow's homelessness service has been transformed over the past decade with the closure of four large-scale, council-run hostels, where homeless people basically lived in warehouses.
"In their place an extensive system of flats and small-scale supported accommodation units has been built up, along with much more work done to prevent homelessness in the first place."
Glasgow – which like all big cities bears much of the brunt of homelessness – has about 2000 units available for emergency accommodation, including temporary furnished flats, assessment centres, smaller hostels, supported accommodation units.
The Crisis report, however, gave a warning about the number of people living in Glasgow streets. It said: "Both rough sleeping and repeat statutory homelessness appear to have declined in Scotland in recent years, probably because of the expansion in the rehousing rights of single homeless people in particular.
"However, anecdotal evidence indicates a recent rise in rough sleeping in Glasgow."
English campaigners praise Scotland's homelessness regime.
However, they warn Scotland – and Glasgow – will not be immune to welfare cuts, especially the so-called "bedroom tax" when tenants could lose housing benefit to cover spare rooms.
Leslie Morphy, chief executive of Crisis, said: "The report is clear that Scotland, as elsewhere in the UK, is likely to face intensifying homelessness pressures over the next few years.
"Last year more than 43,000 households were accepted as homeless by their local council, although we would expect thousands more people will be hidden away from statistics and help.
"The UK Government is sweeping away the welfare safety nets – particularly housing benefit – that have traditionally saved people from the horrors of homelessness.
"Young people are already bearing a disproportionate burden of the cuts and economic downturn, yet the Government seems set to increase the pressure by abolishing housing benefit for under-25s.
"Scotland has led the UK in tackling homelessness by widening its statutory safety net, but to maintain this progress the Scottish Government and councils will need to ensure homelessness and housing remains a clear policy and spending priority next year and going forward.
"And the UK Government needs to rethink its welfare cuts otherwise homelessness may soar – a disaster for those directly affected, and bad for us all."