We've won more councillors, with 431 elected compared to 425 in 2012.
And although the SNP will certainly "win" the general election in Scotland, just as they have the local government elections, they now have cause for concern.
Ms Davidson also went on to criticise Labour, who slumped to become the third largest party in Scotland's councils, adding: "As for Labour, they were left to count the cost of decades of complacency, arrogance and a failure to respond to the concerns of ordinary families".
Launching the party's general election campaign in Manchester, Mr Corbyn warned there will be "a reckoning" if he wins power and breaks up a system he said is rigged in favour of the wealthy and against ordinary workers. The Liberal Democrats, like the SNP, held steady, while the Scottish Greens will be pleased with modest gains.
We have heard all of Ms Sturgeon's lines before - only the SNP will act as a bulwark against the Tories, only a vote for the SNP is a vote for Scotland, and so on.
Looking at results from last week's council election the party thinks it can re-take Glasgow South West.
Scottish Labour, a party that used to weigh its vote in town halls across Scotland, particularly in the West, did predictably badly, now finding itself where the Scottish Tories once languished, unloved and increasingly irrelevant.
The Tory leader hopes to gain a significant number of the 59 Westminster seats north of the border following "very encouraging" results in last week's local government elections.
Voters also backed the Tories in the Borders constituency of Berwickshire, Roxburgh & Selkirk, where first preference votes outstripped the SNP by 20 per cent.
In any event, the change of leadership is likely to create an interesting dynamic with the SNP-run Scottish government, which has frequently been at odds with COSLA in recent years over funding and what councils see as a steady diminution of their responsibilities.
She said: "We will speak up for the millions of Scots who have had enough of the uncertainty and division of the last few years".
There will be at least one new face to this multi-ward after the SNP's incumbent councillor Gail Robertson announced her decision to stand down.
She pledged: "We will demand that politicians of all parties focus instead on the things that matter: restoring excellence to Scotland's schools and getting our economy back to health".
The SNP is claiming victory in Glasgow despite narrowly failing to take overall control of the city council as Labour was ousted from power after almost 40 years.
A meeting of the party's Scottish Executive Committee - which includes Ms Dugdale, Mr Rowley, trade unions and others - agreed Labour would not do any deals which would result in increased austerity for Scotland's poorest people. After all, three years - and an independence referendum - elapsed between the 2012 local elections and the 2015 general election. Not only is the Tory revival real (some Nationalists appeared to be in denial about that), but if some of the swings on Thursday are replicated in Westminster constituencies next month then the SNP could lose some senior figures.
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