Opener Tim Ward has struck a half-century as Tasmania set their sights on South Australia's first innings total in their Sheffied Shield match at the Adelaide Oval.
Tasmania reached 3-105 at lunch on day two, having bowled SA out for 227.
The 24-year-old Ward posted his fourth first-class half-century and is not out 59.
The Tasmanians lost two wickets in Monday's opening session in Jake Doran (11) and Ben McDermott (22).
After the visitors resumed at 1-17, Doran was out slashing a cut shot to Jake Weatherald at gully from the bowling of Wes Agar (1-13).
McDermott nicked Jordan Buckingham (1-31) to wicketkeeper Alex Carey soon before lunch, ending a 59-run partnership with Ward (141 balls, seven fours).
The Tasmanians bowled SA out on day one with pace pair Jackson Bird and Peter Siddle taking four wickets each.
Jake Lehmann (73) and Shield debutant Ben Manenti (59) top-scored for the Redbacks.