Players showing signs of serious brain injury should be forced to retire, former Wales forward Alix Popham says.
Popham, who retired in 2011, was diagnosed with early onset dementia and probable chronic traumatic encephalopathy in 2019.
World Rugby says concussed players will face 12 days on sidelines
What else has World Rugby said?
Dr Falvey said: "Am I convinced that we are doing as much as we can right now? I absolutely am.
"With the data that we've got, we're acting on all the information that we have. Not only that, we're creating our own data. We're the only sport that has done this type of work with instrumented mouthguards.
"We have offered instrumented mouthguards to all the teams in the Premiership, all the teams in the [women's top tier] AP15. We'll be doing the same in the Currie Cup and the Farah Palmer Cup next year.
"We are leading the way in this area so I'm absolutely sure we are doing as much as we can. We will continue to improve, we will continue to work on this and as the information becomes available we will act on it because we don't stand still, I'm absolutely sure of that."
Falvey said he would not rule out changes to the laws of rugby in order to protect players at all levels.
Asked whether limiting the weight of players was an option, he said: "Certainly. We've seen that done quite successfully in the North Island in New Zealand because of some of the differences in children developing at a faster rate than others in their own age group.
"Realistically, everything should be on the table here - anything we can do in a manner that makes it safer to play the game and more attractive to play the game that allows people to get the benefit of being out there with the team."