Compton, guesting for Worcestershire at their New Road ground, scored his second fifty in a week against Australia after making 81 for Somerset at Taunton.
The grandson of England great Denis, Compton has been opening alongside England captain Alastair Cook in recent Tests.
But, after struggling for runs in the home series against New Zealand, he was told by national selector Geoff Miller that Joe Root, currently a middle order batsman for England but an opener with Yorkshire, was the man England wanted to partner Cook against Australia in next week's first Test at Trent Bridge.
Compton, however, is trying hard to force a re-think and this latest fifty against Australia was watched by James Whitaker, a member of England's selection panel and a former Test batsman.
In all, Compton faced 181 balls and scored 10 boundaries before, struggling for fluency, he was caught at mid-wicket off Jackson Bird.
Compton's innings helped Worcestershire end the second day on 246 for seven, 150 short of Australia's 396 for four declared.
Bird, looking lively late on, finished the day with four for 38.
Earlier Steven Smith scored eight fours and a six as he became the fifth member of Australia's top order to pass fifty. He was on 68 not out when captain Michael Clarke declared.