A global tax data sharing programme, which Switzerland is set to implement from 2018, could trigger a fresh round of outflows, especially from emerging market depositors.
Switzerland's private banks are close to ridding themselves of undeclared European accounts, a salutary process but one which has undermined efforts to grow their businesses.
Following the financial crisis, cash-strapped governments chased accounts hidden at banks in Zurich, Geneva and Ticino where wealthy Europeans had taken advantage of Switzerland's famous bank secrecy rules.
Stunned by arrests of high-profile clients for tax evasion, large numbers of European citizens have joined voluntary disclosure programmes and pulled cash from Swiss banks to pay penalties and clear back taxes.
After billions of Swiss francs in withdrawals, recent figures from UBS suggest the tide is beginning to turn.
In the first three months of 2015, the Zurich-based bank reported its steepest quarterly net percentage rise in European assets in over three years. That has helped to justify the bank's decision to refocus on wealth management and slim down its investment bank.
"For the industry, and in particular UBS, the bulk of the European cross-border outflows may be behind us," said Kinner Lakhani, an analyst at Citi.
Wealth in western Europe is expected to grow more slowly than the global average in the coming years, according to a Boston Consulting Group study.
But European clients are frequently viewed as more profitable because they are willing to pay banks higher fees to manage their often-inherited wealth.
There are still bumps in the road ahead for Swiss banks.
A global tax data sharing programme, which Switzerland is set to implement from 2018, could trigger a fresh round of outflows, especially from emerging market depositors.
An end to European withdrawals however, would make it easier for banks to grow the amount of assets they manage. In recent years Swiss private banks have had to drum up fresh business simply to offset the amount of withdrawals.
Clearing the books of undeclared accounts has been no small task. One prominent Swiss banker estimates that they made up more than 80 percent of many banks' assets prior to the financial crisis.
But at the end of 2014 some 95 percent of German assets with Swiss banks had been declared, according to the Swiss Bankers Association. The industry group expects this to reach 100 percent by the end of 2015.
France, Britain and Austria have also given taxpayers the chance to disclose undeclared accounts.
Italy last on list
Bank secrecy in Switzerland for foreign account holders was effectively when the country signed up to the Organisation for Economic Cooperation and Development's (OECD) tax data sharing programme last year.
But its legacy will haunt the industry for some time yet.
Earlier this year, leaked files suggested HSBC's Geneva-based private bank may have enabled clients to conceal millions of dollars in assets in years past.
HSBC this month agreed to pay Geneva authorities 40 million Swiss francs ($43 million) to settle a money laundering investigation at the bank.
Banks have reacted by overhauling their business models, devoting more resources and jobs abroad, particularly to Asia, which is the world's fastest production line for multi-millionaires and billionaires.
Switzerland's banking expertise has helped it to retain its position as the largest offshore wealth centre with $2.4 trillion in assets as of 2014 according to the Boston Consulting Group. But the withdrawals have been a major challenge.
Martin Schilling, a director at accounting firm PricewaterhouseCoopers, estimates that between 350 billion and 400 billion francs have left Swiss banks since the financial crisis, with the majority going to other European countries.
"Over the next one and a half years or so, another 50 billion to 100 billion francs could follow," Schilling said. "Then the situation should largely be settled."
A voluntary disclosure programme with Italy was signed in February and is scheduled to run until September. Banks say this will likely be the last major western European market to pull significant assets from Switzerland.
Recruitment experts say the decline of European withdrawals will boost hiring at home.
Stephan Surber, finance specialist at recruitment firm Michael Page said: "The stronger demand for personnel of the big banks has set in over the last 12 months after they went through a transformation phase for many years."
(Additional reporting by Oliver Hirt)