Gieschen said a free kick against key forward Drew Petrie with around eight minutes remaining and a free not paid to skipper Brent Harvey in the final minute of the game were both correct calls.
Petrie's penalty for high contact on opponent Heath Grundy was given as the two players jostled in a marking contest in North Melbourne's forward line.
But the umpires boss said only the Kangaroos player infringed enough to warrant a free kick.
"Leading into it as they were both coming for the ball there was some engaged contact there, but probably not enough for the umpire to say there's a clear and definite hold," Gieschen told afl.com.au.
"We then see the arm go around the neck, Grundy was taken high, that's what the umpire saw and correctly paid a free kick for that."
Later, with the Swans leading by a point in the final moments of the game, Harvey's jumper was grabbed by Sydney defender Rhyce Shaw as the pair fought for the ball inside North's attacking 50.
"This is a really tight one," Gieschen said.
"You see Harvey take possession of the ball, Shaw grabs his jumper at about that time, and the ball is released.
"Providing that Shaw lets go almost immediately, we don't have a major problem with it."
Press the play button above for more on the two decisions.
