But state attorneys suggested to the same judges who drew those lines -- which effectively set whether a district elects a Republican or Democrat -- that a lengthy and expensive court case could be over if the GOP-controlled Legislature ratifies those maps into law.
Some lawmakers predict they'll approve the maps soon as the next two weeks.
"I think that's the result," said David Mattax, who represents the Texas attorney general's office, when asked by a three-judge panel whether legislative adoption renders an ongoing redistricting lawsuit moot.
A coalition of minority rights groups and Democrats sued the state in 2011 after the GOP pushed newly drawn political boundaries through the statehouse. A San Antonio federal court threw out those maps, which a separate federal court in Washington later found to contain evidence of discrimination.
Texas Republicans have since all but given up on their maps, and now want to permanently adopt boundaries drawn by the San Antonio court to get through last November's elections.
Under those maps, Republicans still preserved solid majorities: They hold 95 of 150 seats in the Texas House, 12 of 31 in the Texas Senate and 24 of 36 seats in Congress.
Perry has made adopting the maps the only order of business so far in a 30-day special legislative session, which began immediately after the regular 140-day session adjourned Monday.
Minority rights groups complained to judges Wednesday that Perry's narrow mandate only allows the Legislature to approve the interim maps and not consider changes. Among their beliefs is that Texas' shifting demographics demands at least two more congressional seats that would be safely decided by minorities.
Observers in the courtroom included Democratic U.S. Rep. Mark Veasey, who, under the court maps, won one of four new congressional districts awarded to Texas because of its surging population. That growth was dominated by Hispanics, and overall, nearly 9 in 10 new Texas residents the last decade were minorities.
A House redistricting committee is scheduled to hold its first hearings Friday and Saturday.
"If the Legislature does not open up its process and do a traditional redistricting, we will find ourselves challenging the map once again and potentially putting the 2014 election in jeopardy," said Democratic state Rep. Trey Martinez Fischer, a member of the redistricting committee.
The dragged-out fight over redistricting last year delayed party primaries into summer and wreaked havoc on political races.
Michael Li, a Dallas attorney and redistricting observer who attended Wednesday's hearing, said another postponed primary is unlikely for 2014. He recalled that slowing down the process last time was in part because the state appealed its thrown-out maps to the U.S. Supreme Court.
"In this case, the state is happy with the interim maps. And legislators and members of Congress, at least on some level, are happy," said Li, who closely follows the issue on his website txredistricting.org.
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