The way the Astros have started to swing the bats, Rodriguez could be pitching with a cushion in his next outing.
Rodriguez looks to win his fourth straight decision over the San Diego Padres on Monday night at Minute Maid Park.
With a 5.46 run-support average second on the team to Bud Norris' 5.92 Rodriguez (6-5, 3.29 ERA) really can't complain about an Astros offense that's averaging a middle-of-the-road 4.2 runs.
However, three of the left-hander's defeats have come in Houston shutout losses.
In Tuesday's 2-0 home defeat to Kansas City, the Astros (30-42) were 0 for 6 with runners in scoring position and left nine on base to waste Rodriguez's seven innings of two-run ball.
"I felt great, but we missed a lot of opportunities to get some run support," Rodriguez said. "That's what happens sometimes."
Rodriguez is 3-0 with a 2.00 ERA in his last four starts against the Padres, whom he hasn't faced since 2009.
Houston followed Rodriguez's latest loss by totaling one run in dropping its next two, but scored 15 while beating Cleveland on Saturday and Sunday.
Left fielder J.D. Martinez hit a two-run homer in each of the weekend wins, while third baseman Chris Johnson went 5 for 8 with a home run, two doubles and five RBIs.
"I feel like I have a good plan right now," Johnson said. "I feel like I'm just trying to make sure I get my pitch and hit it hard and things are falling in."
Johnson is hitless in six at-bats against Monday's scheduled starter Ross Ohlendorf (1-0, 4.50). The right-hander will make his fourth appearance and second consecutive start - after signing as a free agent June 4.
Starting for the first time since Sept. 27 while with Pittsburgh, Ohlendorf yielded three runs in 4 2-3 innings of a 6-4 loss at Oakland on June 16. He did not give up a hit in the first three frames.
"I thought I saw the ball creeping up in the zone a little bit in the latter part of his outing," manager Bud Black said. "They took advantage of some balls out over the plate but overall he hung in there. Maybe not as efficient as he would like."
Ohlendorf has been anything but efficient in nine career starts his most against any opponent versus Houston, going 0-6 with a 5.96 ERA.
After taking two of three from Seattle over the weekend, the Padres (26-47) will not have first baseman Yonder Alonso in the starting lineup for a second straight contest as he continues to rest his sore left knee. Jesus Guzman is expected to start in Alonso's place.
If Astros second baseman Jose Altuve can't go after leaving Sunday's 7-1 victory with a strained right hamstring, Brian Bixler could get the nod from Mills.
Padres outfielder Chris Denorfia is batting .381 (16 for 42) during a career-best 11-game hitting streak.
The Astros, going for their first three-game winning streak since a four-game run May 21-25, split four games with San Diego at Minute Maid last season.