Gloucestershire 114 for 2 (Brathwaite 60, Bracey 46*) trail Hampshire 470 (Alsop 149, Holland 114, Dawson 65, Vince 52) by 356 runs
James Bracey once again underlined his Test credentials in front of England batting coach Marcus Trescothick to help Gloucestershire lay a solid platform in response to Hampshire's big first-innings total.
Bracey and Kraigg Brathwaite put on 88 for the second wicket before the West Indies opener fell late in the day for 60 to leave the visitors on 114 for 2 at the close, having earlier bowled out the hosts for 470.
Bracey, who was named as a reserve batsman for England's tour of Sri Lanka earlier this year, was 46 not out against a strong Hampshire attack spearheaded by Mohammad Abbas, Kyle Abbott and Liam Dawson, with Tom Lace yet to score.
Things looked ominous for Gloucestershire when skipper Chris Dent fell for six to Abbas to a ball that kept low and pinned him on the crease.
But Brathwaite and Bracey, watched from the boundary by Trescothick after scoring 118 and 83 in the win over Somerset last week, calmly saw off the new ball.
With the pair looking relatively untroubled, Liam Dawson then managed to get a ball to spit off the surface and had Brathwaite caught by Lewis McManus.
It led to a tense passage of play but Bracey and Lace survived despite the presence of several fielders around the bat for Dawson's final three overs.
After starting the day on 292 for 3, Hampshire lost nightwatchman Mason Crane early before Tom Alsop fell before lunch for a superbly made 149 - one shy of his highest score. Alsop, who made a century against Leicestershire two weeks ago, struck 19 fours in his 290-ball vigil before being caught down the leg-side by Bracey off Ryan Higgins.
James Vince hit a trademark sumptuous cover-drive to the boundary before lunch on his way to a half-century. The Hampshire skipper wasn't at his fluent best in his innings, but still showed glimpses of class, including successive fours off the bowling of Dan Worrall. However, in a dramatic over, Vince inside-edged the very next delivery to Bracey, with McManus then controversially dismissed to what appeared to be a bump ball, putting Worrall on a hat-trick.
The Australian seamer who was the pick of the visiting bowlers, claimed his fourth wicket when Abbott was struck on the pad as the hosts lost 3 for 16 after the restart.
Dawson smashed two sixes and five fours on his way to an entertaining 65 before being cleaned up by Higgins, who then bowled Abbas to finish with 4 for 78.