Earlier this week, a councillor in the Scottish Borders said she believed people were being short-changed by the rollout of the service.
BT has said it has invested heavily in providing services in areas where it was not commercially viable to do so.
It has also pointed out that there are a wide range of factors at play in determining the speeds received.
The BBC Scotland news website asked for your experiences of the service in the Borders and Dumfries and Galloway.
Iain Rennie emailed: I live in the village of Ednam. Barely 2 miles from Kelso. We get a max of 1.5Mb.
It is frustrating in the extreme to see constant TV adverts for high speed broadband when ours is too slow to stream or watch BBC iPlayer etc.
As far as I'm aware there is no date or plan to upgrade this area.
Byron Raistrick, of Ruthwell, emailed: Since the announcement by the Scottish Executive that the initiative was up and running, I've not seen any evidence of the Â£126m being distributed fairly and efficiently to the areas that need it most - rural locations.
Major cities such as Glasgow and Edinburgh would have been upgraded as a matter of course by BT Openzone to cater for the businesses there and in turn the residential areas would have benefited, yet (they) have been upgraded first with the money.
Linda Lonsdale emailed: We pay extra money to get superfast broadband and it is not any faster load of rubbish conned again.
Susan Cook emailed: Broadband speed in our village  0.9Mb and sometimes even lower. We have been told by BT that it will be four to six years before we get anything better! And we pay the same as all their other customers.
There are  people living in the Borders other than in Melrose and Galashiels yet no consideration is given to them.
Siobhan Liehne emailed: We live on the Mellerstain Estate near Gordon. We keep reading of ministers complaining that constituents in some Borders areas are "only getting 2Mbps". Frankly I would give my eyeteeth for that kind of speed.
We get 0.7 Mbps if we are lucky and sometimes it drops out altogether. Then we have to see signs up telling us that towns only a very short distance away are getting superfast. When we ring BT to try and find out when things are going to improve we get someone in India telling us that it must be our computer.
If it is, then it's every computer on the estate, no matter how new it may be.
Andrew Gray emailed: I live near Chirnside in the Scottish Borders which is enabled for fibre broadband. However only those residents who live within a mile of the cabinet can get anything like the speeds advertised.
My house is two and a half miles from the cabinet so the fibre signal does not reach it at all. According to most comparison websites (including BT's) I can receive broadband speeds of up to 40Mb but in practice I get just over 2Mb, if I'm lucky.
There should be further scrutiny of how public money has been spent on improving broadband services, particularly in rural areas, to ensure that everyone can benefit in the future.
Henry Sinclair emailed: I live in Earlston and have what the major players call "superfast" broadband - ie fibre to the cabinet, which is 100m away or just over 200m of copper wire.
The actual speeds I get vary between 20 and 70Mbps download and 15 to 20Mbps upload.
My grandson who lives no more than 400m from me and 300m from a cabinet can only achieve a max of 6Mbps and pays the same as me.
Copper is a 19th century answer to a 21st century question but BT continues to squander taxpayers' money on using it to provide an inadequate or in some cases no service while the solution is staring it in the face.  As the internet moves from a consumer model to an interactive one the pathetic download speeds and risible upload speeds will hold us all back and eventually our interconnection system will have to be re-engineered using fibre.  Why not do it now rather than throwing billions at a known fatally flawed approach?
Brian Telfer emailed: I have had issues since BT started to enable the Hawick exchange well over a year ago. I was getting better speed and reliability before the exchange was enabled for fibre.
I am now on fibre at double the price, with continual buffering drops in service and regular visits from engineers who contradict each other - speed can be from 1.52Mb to 20Mb - not the 52 Mbps I am paying for.
Uploads are a joke - I now use my phone tethered to the computer to upload anything!
Peter Dorward emailed: I read your report with interest particularly the part that referred to over Â£8m being invested in super fast broadband by SBC and that 94% of homes will have it.
At the moment why not focus attention on getting something like 'normal' broadband speeds to all households.
We have struggled at trying to conduct work when at home when only being able to access broadband internet with speeds that are barely any better than a dial up service!
Any pressure that can be brought to get us to first base is welcomed.
Carole emailed: We live in Bonnington Road in Peebles in a modern house and our broadband speed is very poor we are with BT and get 2Mb which is a joke. Believe one of our neighbours gets better speed. When you try to raise it with BT you don't get anywhere. Poor show ... what's fibre optic? Even a bit better speed would be appreciated fibre optic is a dream for us.
David Jeffrey emailed: I work in broadband provision for local councils in the south of the country. I believe the councillor is correct in her assertion of expecting speed provision to be constant.
Both BT and the industry are living in the last century of squeezing the last penny of investment out of the copper infrastructure in the ground.
Admittedly fibre is not cheap, but the trial in York proves that fibre to the home is achievable with the right partnerships (CityFibre, Sky and TalkTalk in that case)
Digital Scotland should be delivering more, but as long as BT have the monopoly over the infrastructure, nothing will change.
However, this constant and reliable speed will come at a cost, and there is the rub. Will subscribers pay for it?
I expect not. It is worth noting that businesses in south of Scotland (and anywhere else in rural UK) have enjoyed fibre services for many years, but have had to pay top whack for the privilege.
Brian Heslop emails: I live in Sanquhar, Dumfries and Galloway. We're on a farm, so were considered too remote for coverage, the cabinets are located within a few hundred yards of the exchange so the cabinet is still 2.5 miles from the house.
As the exchange is one where the one broadband provider is BTopenreach, so all the advertised cheap offers from EE, TalkTalk, Sky etc are not available. So the double hit of slow broadband and the highest prices.
Part of the problem is the politicians not understanding what BT are selling them, it was never going to give a good service to all, using an urban solution in a rural environment.
Lindsay Lewis emailed: We are lucky if we get 1.5Mb because we are several miles from the exchange.  BT have not upgraded our exchange (Yarrow)  and seem unlikely to do so.  Why?  Because there aren't enough people/customers to make it worth their while.  It is a disgrace - we pay the same as someone getting up to 50Mb, and what makes it even more galling is that BT are continually sending us marketing material urging us to sign up to BT Infinity!  So for the foreseeable future we will continue to live in the digital dark ages.
Jason W emailed: BT need to wake up and smell the coffee.
Copper phone lines are dead assets - they will need to be replaced with fibre optic right to the premises sooner or later. If the cost of upgrading to actual fibre to the premises wasn't so outlandish, I'd do it in a heartbeat.
The speed of broadband in southern Scotland has provoked some intense discussion.