The club signed Augie Ojeda, who was eligible for salary arbitration, to a one-year deal worth $712,500.
"We're happy to keep him in the fold," Byrnes said. "Obviously, he had his rights in the arbitration system. He's been a terrific utility guy, and when he's had to fill in at second base, he's done an admirable job. And as we continue to figure combinations at second, some of them could involve him. Glad we got that piece of business done and we will continue to move on."
Part of that moving-on process was a one-year offer to infielder Felipe Lopez, who hit .283 with a .343 on-base percentage last year with the Nationals and Cardinals. Lopez, who like Ojeda is a switch-hitter, can play any position in the infield and also has played both corners in the outfield.
It is not known how much the offer is worth, but it is likely a good deal less than the $4.9 million the 28-year-old made last year. Lopez hit .234 before being released by the Nationals on July 31. Less than a week later, the Cardinals signed him and he hit .385 for them.
"We've had productive discussions so we'll keep chipping away at it," Byrnes said of filling his hole at second and not about Lopez specifically.
As for Rhodes, the D-backs spoke with his agent Dan Horwits again on Wednesday and are waiting to hear back.
"Steady dialogue but nothing to report," Byrnes said.
Even if Rhodes or Lopez were to agree to terms before the teams head home after Thursday's Rule 5 Draft, a deal would not be finalized until later as any player would need to pass a physical.
Finding a second baseman and a left-handed reliever has been the focus of the D-backs here in Las Vegas.
"Other than that, it's just general stuff and some ideas," Byrnes said.
The team planned to talk Wednesday night about possibly selecting a player in the Rule 5 Draft. One rumor making it's way around the lobby is that the team is interested in selecting first baseman/outfielder Jordan Brown from the Indians' system.
A fourth-round pick in the 2005 First-Year Player Draft, Brown won the Class A Carolina League's Most Valuable Player Award in 2006 and the MVP for the Double-A Eastern League in 2007. With the Cleveland system stocked with corner outfield/first-base types, Brown was not added to the 40-man roster this winter.
It's likely the D-backs would need to trade up from their spot at No. 15 to get Brown. Teams can buy picks from other teams or trade players for it, though it didn't sound like that was something Arizona was interested in doing.