"I've made one phone call already this afternoon and plan to make another on [Wednesday]," Luhnow said. "Oftentimes, players coming off a long season want some time to rest, but that doesn't mean we can't be negotiating and trying to get a deal done. We're going to work hard to get these guys done as soon as we can."
The Astros have four picks among the top 10 rounds still unsigned -- Fontana, Tucker, fourth-rounder Rio Ruiz (third baseman from Bishop Amat High School in La Puente, Calif.), and catcher Tyler Heineman of UCLA, which was still alive in the College World Series as of Tuesday.
Luhnow said the sequence of how you sign players -- for example, signing the higher Draft picks earlier than lower picks -- matters when it comes to financial obligations and staying within the allotted bonus pool.
"Nobody wants to get to a point where you have to sign somebody to risk losing a pick, or you're not able to sign somebody because you risk losing a pick," Luhnow said. "There's definitely a sequence that matters, and I've gone through every situation of who we should sign and when."
Luhnow hopes to have another deal done with a top pick at some point during this homestand.