Galvis pleaded for more netting last August, when he hit a foul ball that struck a girl in the face.
"A little bit over the dugout and I think more people are going to be safe," Galvis said on Wednesday. "The last couple of days, I think I saw like one guy get hit on the other side [of the netting]. But this is a good start. Let's see what it brings and go from there."
In February, the Phillies invited season-ticket holders with seats behind the dugout to view their seats with the new netting. One hundred seventy-five people showed up. The Phillies said nobody cancelled their tickets, and only 10 season-ticket holders asked to be relocated.
"Since we started playing, we've had no complaints," Phillies executive vice president and chief operating officer Mike Stiles said. "The comments that we're getting right now is, 'It's not interfering with our ability to watch the game,' and, 'We appreciate being behind the netting.'
"Our players have been good about flipping balls lightly over the netting so they're still getting some foul balls. It's been a very positive experience. It was the right move, and I think we did it the right way giving people an opportunity to come look. If they wanted to move, they could."
Galvis said perhaps the netting could extend even further down the line. Asked if that could happen in the future, Stiles said the Phillies will continue to look at it.
"Whether we go up a little higher, whether we go out a little further, that remains to be seen," Stiles said.
But Galvis will take what is there.
"I don't know if it was because I said something, but at the point right now I feel good, because people come here with their families and they're protected right now, especially young kids," Galvis said. "I think right now there's more safety. You hit one into the net, OK, that's over. We have the net right there and you can keep your focus on the game."
Todd Zolecki has covered the Phillies since 2003, and for MLB.com since 2009. Follow him on Twitter and Facebook and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.