(Reuters) - Texas Governor Greg Abbott has signed into law a more relaxed version of state voter-identification requirements than a previously enacted measure struck down by U.S. courts as racially discriminatory. The new measure was designed to remedy flaws the courts found in the original law by providing Texans an alternative to the type of government-issued photo ID they had been required to present in order to vote at polling stations. Voters will now be permitted to cast their ballots by furnishing some other documentation bearing their name and address, such as a bank statement or utility bill, if they also sign an affidavit attesting to having a “reasonable impediment” to obtaining a valid photo ID. Critics contend that the measure, passed by the Republican-controlled legislature last month and signed on Thursday by Abbott, a first-term Republican, is still aimed at discouraging racial and ethnic minorities, who tend to favor Democrats. They particularly object to provisions carrying a prison sentence of up to 10 years for lying on a voter-ID affidavit. The list of valid photo-IDs accepted under both the previous law and the revised measure includes a driver’s license, U.S. military identification, U.S. passport and concealed handgun permit, but not a student ID card. Texas ranks as the most populous Republican-dominated state, with the Republican Party winning every statewide race for elective office for more than 20 years. But shifting demographics have given hope to Democrats that they can eventually turn the state to their column. The original voter ID requirements were signed into law in 2011 by then-Texas Governor Rick Perry, a Republican. Considered one of the nation’s strictest such measures, it has been subject to years of court challenges, with the law’s opponents saying it could exclude up to 600,000 voters. Supporters of such laws have countered they are necessary to protect the integrity of the election system, despite little evidence of actual voter fraud. The U.S. Supreme Court declined in January to hear an appeal by Texas seeking to revive the original law’s requirements.     