Michael Surface faces trial later.
Both pleaded not guilty last month in Houston. Prosecutors had sought to try Eversole and Surface together.
Prosecutors allege Eversole accepted $63,000 to buy a home and more than $43,000 to purchase antique firearms.
Eversole was indicted on charges of conspiracy, receiving a bribe and two counts of filing false tax returns.
Surface was indicted on charges of conspiracy and paying a bribe.
The men, if convicted, face up to 10 years in prison.
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The Associated Press contributed to this report
