THE 113TH Congress, which wrapped up at the end of 2014, was not quite the worst in history. According to one measure — the raw number of initiatives passed — it just barely beat the 112th, which set a modern-day low well below that of the do-nothing Congress Harry Truman beat up in 1948. Suffice it to say that the past four years have been pretty dismal on Capitol Hill.

But this year’s new Congress does not have to follow the pattern — and last year’s lawmakers show why.

Before the 113th closed, we highlighted the hard work that many members of Congress put in to drafting bipartisan proposals that would address a range of unspectacular but pressing national problems. Their labor did not result in passed legislation. But it provides a basic road map for the incoming Congress, should party leaders decide to work in the national interest.

They could start with the simplest policies on which lawmakers have failed to advance enough. For example, a cybersecurity proposal that the House approved in 2013 would help combat hackers attempting to access private networks — such as Home Depot’s or Sony Pictures Entertainment’s — by quickly sharing information on novel cyberthreats. Congress should ease approval of new trade agreements — including two major pacts on which the Obama administration is working — by restoring “fast-track” trade authority to the White House. A modest, bipartisan energy efficiency bill has languished in the Senate. It’s done and has buy-in from both sides; it just needs a clean vote. These could get done in the new Congress’s first week.

Then there are some knotty problems on which the parties are surprisingly close to final agreement. The housing finance giants Fannie Mae and Freddie Mac require more reform to limit taxpayer exposure and market distortions. Plans emerged last year to tighten up public guarantees of private mortgages by charging fees sufficient to cover the liability.

The U.S. Postal Service faces long-term technological and structural challenges, but Democratic and Republican lawmakers have hammered out balanced plans to reduce the service’s financial burdens in return for sensible streamlining reforms.

The tax code is a complicated mess, and members of both parties have proposed simplifying it by broadening the taxpaying base and lowering nominal rates. A common belief is that tax reform will fail as Democrats demand that the process result in more federal revenue and Republicans balk at the idea. But a lot of work has already been done, and the substantive differences are bridgeable if lawmakers are serious about accomplishing something.

The gas tax also needs to go up and be indexed to inflation, as a bipartisan Senate bill would have done, in order to pay for the nation’s roads. If lawmakers are too cowardly to do the right thing, they have a second-best approach ready: using a one-time windfall from the potential tax reform to pass a medium-term transportation funding bill.

With these and several more areas of potential agreement, the next year will test Republicans’ claims that they finally want to govern responsibly — and Democrats’ claims that they have long been the adult party willing to deal for the public good.