My idea, intended for the UK, but possibly applicable elsewhere, will generate a huge amount of government revenue, complete change immigration, and stimulate economic growth. The idea is a very simple: auction residence visas.The UK is still a fairly desirable place to live. I do not think it is still as desirable as Australia, Canada or the US, but there are more than enough people who like it well enough to make this work.
What I suggest is a charge in the low to mid thousands of pounds for an annual visa, to high tens of thousands to low hundreds of thousands for a lifetime one: I am not sure how much of a premium the security of the latter is worth.
Consider the impact. A million people (i.e. a less than 2% increase in the population) paying £5,000 a year would be enough to pay the cost of servicing the national debt, making the deficit effectively free. Furthermore anyone who found it worth paying that much would have to have an income high enough to pay a substantial amount in tax as well (of course that would need to be netted off against costs, but it would be strongly positive).
There would be some costs, and these would have to be minimised by filtering out some people. I would suggest those with criminal records, criminal connections, and not in good health. Excluding the former would be a significant tightening compared to current visa requirements which, in practice, often welcome rich crooks and criminals.
Alternatively a million people who pay a £100,000 each would pay enough to pay off large chunk of the national debt and would pay even more in tax.
Then consider the economic stimulus that would result. The extra government spending and the extra money being spent by all those extra people would inject a huge amount of money into the economy.
It would also drastically reduce illegal immigration: it is definitely preferable to pay the government and enter legally, free to take any job, than to enter illegally, with no guarantee of success, and no security once in, than to risk paying smugglers.