Conaway first ran for elective office in 2003, when he ran in a special election for the 19th Congressional District, which came open after 18-year Republican incumbent Larry Combest stepped down shortly after winning a 10th term. Conaway lost by 587 votes to fellow Republican Randy Neugebauer. A few months later, the Texas Legislature redrew the state's districts in an effort engineered by then-House Majority Leader Tom DeLay. Three brand-new districts were created, one of them being the 11th, which was based in Midland. Previously, Midland had been part of the Lubbock-based 19th District. DeLay was particularly keen to draw a district based in Midland, Odessa and the oil-rich Permian Basin in part because Texas House Speaker Tom Craddick was from that area. This district is heavily Republican – by some accounts, it was the most Republican district in Texas at the time. Republicans had dominated every level of government since the 1980s, and usually garner 70 percent or more of the vote in this area (Glasscock County had voted 93 percent for Bush in 2000, the highest percentage of any county in the nation). The race was essentially over when Conaway announced his candidacy. He won in November with 77 percent of the vote, one of the largest percentages by anyone facing major-party opposition.