When the Democratic Party's Fairness Commission was convened this summer to rewrite the party's presidential nomination rules, the gist of its instructions from party Chairman Paul G. Kirk Jr. was simple: Do the least you can, the quickest you can.

That was no small order to a party that brought a near religious fervor to four previous rules overhauls in the past 16 years. But as the 51-member commission sits down today and Saturday for its first round of vote-taking following a series of regional hearings this summer, it seems poised to keep faith with Kirk's mandate and shoot only for small fixes.

"Kirk wants it to be quick and clean and I think that's what he's going to get," said Mark Siegel, a veteran party rules rewriter and member of the commission. "Nobody wants a public show for you guys the press and there is a sense that as a party we ought to be focusing on theme and messages, not on rules."

When the panel was created at the party's national convention last year, its mission was cast in a different light. It grew out of complaints from the presidential campaigns of the Rev. Jesse L. Jackson (D) and Sen. Gary Hart (D-Colo.) that the 1984 rules were too heavily stacked for front-runners. Jackson pointed out that he had received about 20 percent of the vote in all caucuses and primaries, but, because of various thresholds and "winner-take-more" schemes concocted by partisans of Sen. Edward M. Kennedy (D-Mass.) and former vice president Walter F. Mondale, he received only 12 percent of the delegates.

Jackson scored plenty of debating points with the grievance, but he has been virtually frozen out of any role in the commission. Hart has roughly a dozen supporters on the panel, but has taken a hands-off posture toward its work -- in part, some suggest, because in 1988 he will not be the long shot he was last year, and thus his interests have changed.

None of the other prospective candidates for 1988 has sought to manipulate the commission either, giving Kirk and his hand-picked commission chairman, Donald L. Fowler, a longtime party activist from South Carolina, a free hand in the proceedings. They have let it be known they will support three changes and will discourage almost everything else.

The three are:

* Thresholds. In 1984 the party raised its thresholds to 20 percent in caucuses and primaries, meaning that any candidate who received less than 20 percent of the vote in a state got no delegates and had his support divided, proportionally, among candidates who exceeded the threshold. Kirk and Fowler want to lower the threshold to 15 percent, where it stood prior to 1984. They are opposed by the Democratic Leadership Conference, a group of centrist elected officials who argue that lowering the threshold would prolong the life of fringe candidacies and hamper consensus-building in the nomination process.

* Closed primaries. Party rules allow only registered or declared Democrats to participate in party primaries and caucuses, a policy adopted in 1976 to keep Republicans from crossing over and casting "mischievous votes." Wisconsin argues that such a declaration of party loyalty runs counter to its nonpartisan political tradition. Kirk wants to address Wisconsin's problem, but does not want to open up all primaries and caucuses, as the leadership conference and others have suggested.

* Selection of congressional delegates. In 1984 three-fifths of Democratic House and Senate members were guaranteed convention delegate slots, and were supposed to go there unpledged. While they complied technically, most made their candidate preference known. Thus, the selection of the House members, in January 1984, became a de facto first caucus. Kirk wants to move the selection process back, so that voters are not upstaged.

Kirk has said that he opposes, on grounds of impracticality, rearranging the voting calendar in a way that would alter New Hampshire and Iowa's status at the front.

He and Fowler oppose a proposal by Democratic pollster Patrick Caddell to offer the incentive of winner-take-all primaries -- currently outlawed in party rules -- to states that hold their primaries at the end of the nominating season.