The Council says "The changes are in response to significant numbers of requests for the extra measures."
Which is very good in lots of way - people care, bother to complain AND get listened to - and some of it is even acted on!
I'm not defending 'the council' - politicians or officials - but I have to (reluctantly!) admit that this is quite an achievement - when it happens...
Things like Buccleuch Street are permanently problematic - "Without demolishing Brazilian Sensation" etc. THAT attitude largely disappeared in the 70s when it was still common to think about knocking down whole areas and starting again - not least in the South Side.
(If you ever see this in a shop for a fiver or so, BUY IT!)

In addition 'we' - Edinburgh/UK/The World are still gripped by the car culture (See today's parking story! - "Parking fees slashed for all-day stays").
In Edinburgh there remains a bigger problem than the council in this sort of thing - the Police . They are responsible for enforcing the limits and if they are strongly against something it is less likely to happen.
This is probably why 'logical' things like Melville Drive aren't likely to be 20mph any time soon. The fact that it (effectively) goes through a public park is 'less important' than the reality that it doesn't have residential/retail frontages and also that it is used more by through traffic than some of the other roads that are due to become 20mph.
I think Melville Drive ought to be 20mph as a matter of politics/principle. The present situation is regarded as satisfactory for pedestrians because of all the "signalised crossings". For cyclists there have been gradual improvements - including the closure of Meadow Place - but it could be better...
20mph might help. It might encourage some 'in a hurry' drivers to avoid it, though the reality is that at most times of the day, the traffic volume must mean that the end to end average speed is well below 20mph.
More could be done.
WHY does there need to be two lanes westbound at this junction? If the (notional) centre line was moved south there would be room for a cycle lane into the ASL!! (AND a cycle lane going to Tollcross - all the way...)
