Tuesday’s release of a 62-point report on boosting participation in U.S. elections and making Congress work offered an appropriate backdrop to an electoral contest unfolding the same day in Mississippi.

The 62-point “Bipartisan Blueprint to Strengthen Our Democracy” came from the Bipartisan Policy Center’s Commission on Political Reform, which spent the past 18 months gathering public input, conducting research and developing its recommendations for fostering a more engaged electorate and a better functioning Congress.

Former Maine Sen. Olympia Snowe, a Republican, was one of the commission’s five co-chairs. She led the panel with two former Senate colleagues, South Dakota Democrat Tom Daschle and Mississippi Republican Trent Lott; Democrat and Clinton-era Agriculture Secretary Dan Glickman; and Idaho Republican Dirk Kempthorne, a former governor, senator and interior secretary.

The five politicians didn’t make any suggestions for radical reform. But they did, wisely, emphasize the importance of greater voter participation in partisan primaries as part of their wide-ranging report.

“The commission believes political parties should be engaged in reaching out to a much wider swath of voters,” the report reads. “The parties must engage more than just a faction within their coalition and should see primaries as a way of attracting the general public to their party’s message and candidates.”

The Tuesday runoff vote in Mississippi’s Republican Senate contest between incumbent Sen. Thad Cochran and tea party-backed challenger Chris McDaniel offered the case in point. On June 3, McDaniel, a state senator, bested the six-term incumbent’s vote count. Three weeks later, Cochran prevailed — though the contest was still close.

His strategy? Largely, growing the electorate, rather than relying on those who typically vote in Republican primaries. About 319,000 people cast ballots on June 3. On Tuesday, more than 375,000 voted.

The result was the victory of a candidate with more cross-party appeal and less rigid ideology than the stridently conservative McDaniel.

In sticking to suggestions that won’t rock the boat, the Bipartisan Policy Center’s reform blueprint didn’t recommend a grand reformulation of the primary itself away from the nexus of party control, such as California’s non-party primary in which the top two vote getters advance to the general election, regardless of party affiliation.

The group’s recommendations for boosting turnout in existing primaries include setting a single date for every state to hold its congressional primaries, opening up primaries to independent voters and members of other parties, and encouraging political parties to set goals for boosting voter turnout in their primaries.

But low voter turnout in primaries is not the nation’s only political ill. Rigged, party-dominated redistricting has made Republican districts even more Republican in recent years and Democratic districts more Democratic. When members of Congress represent noncompetitive districts, they become accustomed to talking to just a segment of the electorate — those voters who turn out for party primaries — and there’s little electoral reward when they work across party lines.

The Bipartisan Policy Center’s solution, true to the center’s name, is a redistricting process with bipartisan buy-in when a redistricting process without partisan involvement would be the better route.

Maine has a redistricting process that enjoys broad, bipartisan legislative support; it involves a commission made up mostly of party members. Last year’s legislative redistricting encountered little legislative opposition. Notably, that process ended with two of the Maine House’s four unenrolled members forced into re-election contests with sitting, party-affiliated legislators by virtue of how their district lines were redrawn.

We appreciate the political reform panel’s thoughtful contribution to the conversation about how the U.S. can break past the gridlock that has stalled Congress in recent years. Reforms that enjoy bipartisan support can help advance the nation’s business. In some instances, nonpartisanship can help advance it more.