The first step has come from the President, within barely 24 hours of his inauguration for a second term and at almost the same moment that a mortified Congress voted to reprimand Newt Gingrich and fine him $300,000 (pounds 180,000) for lying over his allegedly improper use of tax-exempt money.
Still smarting from the furore over the millions of dollars which flowed into his own Democratic Party's coffers from dubious sources last year, Mr Clinton announced a ban on contributions from foreign citizens and corporations, including their US subsidiaries, a $100,000 cap on individual donations and close scrutiny of all contributions over $5,000.
Thus the party hopes to avoid repeats of such 1996 embarrassments as Vice-President Al Gore's participation at a $5,000-a-monk fundraiser at a Buddhist temple in Los Angeles, the $1.5m gratefully accepted by the Democratic National Committee from questionable Indonesian and other Asian sources (only to be shamefacedly returned) and red carpet White House treatment for major benefactors, a couple of whom at least, it later transpired, faced criminal charges.
The embarrassment did not end with election victory: although Janet Reno, the Attorney General, has resisted demands to appoint yet another independent counsel to explore possible White House wrongdoing, Republicans have lined up a battery of Congressional hearings into allegations of corruption. Thus "Indo-gate" bodes fair to join Whitewater, the purloined FBI personnel files and the White House travel office firings among real or imagined Clinton scandals.
But the presidential bid to reclaim the high ground on the issue may prove as cosmetic, and as futile as every other recent attempt to break the addict-like dependency of American politics on money.
It may true, as Roy Romer, the Colorado Governor and new general chairman of the Democratic party, maintains, that the new rules would have cost the DNC $6.5m had they been in effect last year. But that is a drop in the bucket of the stupefying $1.6bn (pounds 1bn) spent on the 1996 presidential and congressional elections.
Another problem is "soft money," the contributions theoretically destined for party organisations which are then channelled into individual campaigns. They generated about $100m for Republicans and Democrats alike in the last campaign. On Tuesday Mr Clinton urged the elimination of "soft money". But Republicans say they will only agree if their opponents forgo the financial help they receive from trade unions, which the Democrats are unlikely to accept.
A bill sponsored by Republican Senator John McCain and his Democratic colleague Russ Feingold of Wisconsin suggests that candidates accept "voluntary" ceilings on campaign spending, with sanctions if they exceed the limit. However, a recent Supreme Court ruling broadly upholds the view that curbs on campaign spending infringe the free speech rights of the First Amendment of the US constitution.