The House Banking Committee is examining just one abstruse and quintessentially Washingtonian aspect of Whitewater - the propriety of informal contacts between the White House and senior Treasury Department officials over the Federal Bank investigations into Madison's failure, between September 1993 and February 1994.
On Friday, the Senate Banking Committee repeats the exercise, broadening it to the other area already dealt with by the special prosecutor, Robert Fiske: last year's suicide of Vincent Foster, the former White House deputy counsel who was a close friend of the Clintons from Little Rock days. But the Senate too, at least in this first segment of the congressional probe of Whitewater, will not get to the meat of the matter.
If Whitewater is a scandal (Mr Clinton endlessly points out that neither he nor his wife have been accused of wrongdoing), the scandal happened in Little Rock. Its heart is the relationship between the ill-fated venture set up in 1979 by the Clintons and Jim McDougal, and Madison Guaranty, set up by Mr McDougal in 1982 and whose collapse in 1989 cost US taxpayers dollars 50m (pounds 33m).
Mr Fiske's investigators are still in Little Rock, combing the books of the two ventures to find out whether they were used as political or personal slush funds for Mr Clinton and sundry members of the close-knit Arkansas establishment. Only when they have completed their report later this summer will Congress conduct its own public hearings into Whitewater proper.
The same goes for Mr Fiske's remaining unfinished business: the removal of documents (believed to relate to the Clinton's involvement in Whitewater) from Mr Foster's White House office by senior aides on the night of his suicide a year ago.
Two more factors will reduce the impact of this phase of hearings. First are the findings published by Mr Fiske last month. After hearing evidence from two dozen White House and Treasury officials, including Mr Clinton, he reported that while some of the contacts might have been ethically questionable, none constituted an attempt at a cover-up, or to pervert justice. As for Mr Foster's death, Mr Fiske is convinced it was a suicide caused by depression, unrelated to Whitewater.
Second, the partisan edge to proceedings can only favour Mr Clinton. The Democrats never wanted hearings in the first place - least of all Henry Gonzales, the crusty 78-year-old Texan who chairs the House committee. And while the Republicans may have the edge in righteous indignation, numbers favour the Democrats. Yesterday, by a 31-19 vote along strict party lines, the committee voted not to go over the circumstances of the Foster suicide after a vintage Gonzales tirade against 'falsehoods, distortions and scurrilous claims' which even Mr Fiske's labours had failed to dispel.
Pit-falls aplenty await the White House. These first hearings will last at least until the end of next week. The Republicans will try to widen their scope and even if they fail, there will be the spectacle of a public grilling of a score or more of senior administration officials, including many members of the Clinton inner circle, and most of the Treasury high command.