DES MOINES, Iowa — Republicans and Democrats in state capitals across the country are talking ambitiously about what they’ll do next year with the unchecked power they amassed in the fall elections. In more states than not, one party now has full control of government.

But you won’t hear much brash talk in Des Moines. Here, party leaders are warning supporters about what they shouldn’t look forward to next year and speaking mildly about compromises.

Iowa inhabits an unusual parallel universe in this politically polarized time. It is one of only three states where control of the legislature is split between the parties. Instead of laying out bold initiatives for overhauling taxes or education, Republican Gov. Terry Branstad and legislative leaders are trying to figure out a few things they can agree on so that when the session is over, they won’t wind up with nothing.

“You don’t always get everything you want,” Iowa Gov. Terry Branstad said in an interview, in what could serve as the legislature’s rallying cry.

At a time when other states are pursuing purer — and often diametrically opposite — visions of how government should work, Iowa will likely take some from Column A and some from Column B, in an approach that could later provide a hybrid counterpoint to the more ideological ventures.

At very least, Branstad said, citizens “don’t get some of the excesses that you don’t want.”

In the fall elections, Republicans won veto-proof majorities in many of the 26 state legislatures they already controlled, which will allow them to roll over any opposition. Democrats also gained concentrated strength. Half of state legislatures now have such “supermajorities,” up from 13 only four years ago.

So armed, Republican-dominated states like Kansas and Oklahoma will aim to cut their income taxes to prove the conservative argument that the economy will benefit even if public services suffer. Republicans in Wisconsin hope to stimulate mining with relaxed regulation. Tennessee, Texas and others will pursue a more loose-knit version of public education, replete with independently run charter schools and cash vouchers.

But Republicans in Iowa won’t be going there.

The GOP kept control of the 100-member House in November, but only by four seats. Democrats held the Senate held by the narrowest of margins, 26-24.

“We better sit down and start talking and be more serious about accommodating each other interests,” said Senate Democratic leader Mike Gronstal.

While other Republican states are in action mode, Branstad has named the head of the Democratic-leaning state teacher’s union to a new task force studying how to improve schools.

Gronstal said Democrats will work with Branstad on an education initiative to base teacher advancement more on merit and results. The goal is to boost performance without remaking the whole system.

He said the Senate will also give a new look at business-friendly property tax changes, which Democrats torpedoed last year.

“We all have a set of things we want to accomplish, but our shared focus is to continue getting Iowans back to work,” he said.

Branstad and Republican House Speaker Kraig Paulsen say Iowa’s improved economy has eased some of the budget pressure of the past four years, enough to open a discussion of higher spending for education and job protection for public workers. The state’s unemployment rate of 5.1 percent in November was the fourth-lowest in the country, the result largely of what has been a stable farm economy.

Divided government isn’t a new experience in Iowa. Although Republicans dominated in the late 1990s and Democrats did six years ago, balance has been the norm. The state has had one Democratic and one Republican U.S. senator for 28 years (Tom Harkin and Chuck Grassley, respectively). During that time, Iowa had a Republican governor — Branstad — for 16 years and a Democratic governor for 12. The four House seats are split evenly.

Iowa’s redistricting process is a factor. Unlike in other states, the congressional and legislative maps are drawn by a team of non-partisan analysts rather than legislative committees. Thus, the results more accurately reflect the state’s partisan balance.

Again in this election, “For better or worse, the electorate did not say, ‘OK, one party, we’re going to take your philosophy on everything and ignoring the other,”’ said David Roederer, a veteran Branstad adviser and Iowa’s budget director.

The parties took a more partisan tack in the last legislative session, with the result that, other than passing some pressing budget control measures, little else was accomplished. Gronstal says 2013 provides a ripe opportunity for compromise before the approaching 2014 elections heighten partisan tensions. Branstad, who was governor in the 1980s and 1990s before running again in 2010, is expected to stand for re-election.

Except for lawmakers in Kentucky and New Hampshire — the other two states with divided legislative control — those elsewhere can barely imagine what Iowa expects to experience. In Oklahoma, where Republicans hold every statewide elected office and supermajorities in the House and the Senate, Democrats weren’t invited to the budget talks with the governor’s office. In Minnesota, where Democrats won both chambers this year and hold the governor’s office, Republicans are expecting a parade of Democratic policy initiatives.

“There isn’t really anything we can participate in unless asked,” said outgoing Minnesota House Speaker Kurt Zellers, a Republican.