Haryana's bowlers failed to impress in the morning session as England XI scored briskly to reach 136 for no loss at lunch on the opening day of their final practice match in Ahmedabad on Thursday.
Playing the last of their warm-up games before the four-Test series against India starting November 15, the English seemed at ease with the conditions after electing to bat first in the four-day game.
The two negotiated the Haryana attack rather smoothly with Cook striking 17 boundaries in his 98-ball effort so far. Compton proved perfect foil for his skipper's aggression, hitting six boundaries in his 73-ball stay at the crease so far.
For Haryana, it was a thoroughly disappointing session with none of the bowlers failing to trouble the batsmen.
Medium pacers Sanjay Budhwar and Sachin Rana were the only ones who managed to keep the scoring rate in check.
Budhwar conceded 39 in his nine overs, while Rana gave away just 21 in his seven overs, which included two maidens.
The team did itself no good by giving away as many as 11 extras during the opening session itself.
Photograph: Gareth Copley/Getty Images
PIX: Meet Sanjay Dutt's adorable twins!
'I was desperate to spend quality time at the wicket'
Let Sachin decide his retirement: Kapil Dev
Photos: Cook leads England fightback vs India 'A'
England look to ace spinners in tour game vs Haryana