In both instances, Smith faced a short ball from the left-arm quick which struck him high on the body before trickling behind the wicket.
Under cricket’s laws, a leg bye can only be scored if the umpire is happy a shot has been attempted or the batsman has attempted to evade the ball.
Umpire Llong both times ruled that Smith had left the ball and let it strike him rather than “try and avoid being hit” in an absorbing first session in which Australia lost 2-67.
Smith made a beeline for Llong when lunch was called and the pair had an animated discussion for several seconds while walking off the ground.
“I was just asking the question,” Smith said.
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It came after Matthew Wade frequently let the ball strike him on the body in the first Test in Perth, once also denied a leg bye when the umpires claimed he hadn’t played a shot.
“I don’t think I am as mad a Wadey is, last game just trying to let them hit him,” Smith said.
“I was trying to get out of the way of them. It’s his interpretation and I’ve got to back that.
“I’ll just keep playing, I don’t want to get stuck into anything.
“His interpretation. Fair enough, play on.”
It came as Smith tried to find a way to counteract Wagner’s barrage of short balls, with fields set to catch him out on the pull shot.
Smith has been caught pulling the ball in his past three Test innings against the Black Caps, as well as when they last met in a one-day match during the World Cup.
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However, he played the short ball without giving any real chance on Boxing Day, going to stumps unbeaten on 77 with Australia 4-257.