Dempsey ended day one in seventh before moving up to third after day two and his progression continued as he is now one place higher with three races taking place on day three to make it eight complete in total.
The 32-year-old, who won silver at London 2012 last summer, finished second in his first outing in Buzios and, despite a 15th during the next race, he ended the day with a win.
That win was Dempsey's second of the regatta while of his eight races so far he has finished second three times with his 15th now becoming his discard.
Dempsey has 21 points to his name with Olympic champion Dorian van Rijsselberge now leading with 15 after a first and two seconds from his day's work in Brazil.
Fellow Brits Elliot Carney and Tom Squires are 23rd and 27th respectively while, an outstanding day's racing from Lee-El Korsiz, saw Shaw drop from first to second in the women's fleet.
Leading by three points after day two, Shaw could only manage a 12th, a second and a sixth 24 hours later as Israeli Korsiz dominated the fleet to win all three of the scheduled races.
That has had a significant impact on the overall standings with Korsiz leading with 17 points and Shaw 13 behind in second before another Israeli, Maayan Davidovich, in third another seven adrift.
Much like Dempsey, Shaw, who won Olympic bronze at Beijing 2008, is joined in the women's fleet by two other Brits with Izzy Hamilton 15th overall and Claudia Carney 29th.
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