England drew their pre-Test warm-up against Bangladesh A but another failure for Kevin Pietersen meant they left with the same major problem they arrived with three days ago.
Pietersen's lack of form is fast becoming the story of the tour but, after compiling just 49 runs in six innings before today, he managed just 20 more before being bowled on the sweep by Mohammad Ashraful.
England, whose second innings ended on 185 for five in nominal pursuit of 284, had earlier accelerated the game by offering the hosts nine overs of pitiful declaration bowling which were taken for an astonishing 189.
That decision must have been, at least in part, designed to hand Pietersen some much needed time in the middle - but instead Cook (43 retired) made most use.
Michael Carberry's prospects of a Test debut on Friday must hang in the balance after he looked in good touch before falling for an inconclusive 25.
Carberry launched the chase in brisk fashion, smashing Dollar out of the attack with figures of 3-0-29-0.
But, after dominating an opening stand of 57, he fell to the spin of Ashraful to bring the under-pressure Pietersen in.
Having succumbed for five in the first innings, Carberry's failure to register a sizeable score may have ended the debate over England's batting line-up, with Jonathan Trott now favourite to open the innings with Cook.
Pietersen looked to start positively and when Mehrab Hossain was tossed the ball immediately after his arrival at the crease the pressure was on.
Pietersen's vulnerability to left-arm spin has been much talked about in recent days and he edgily squirted Mehrab's first ball into the off-side.
He appeared to find his feet thereafter, picking up two fours and mighty six off Ashraful, but it was not to last.
After 22 minutes and 23 balls in the middle he missed a sweep off Ashraful and was bowled, again denying him some much-needed batting time.
Cook has been in the sort of consistent form Pietersen must envy since taking charge of the side and he progressed serenely against both spinners and seamers before retiring seven short of 50.
Bresnan was promoted to number four - an indication perhaps that he will be required on Friday - and pushed his way to 36 before becoming Ashraful's third wicket.
James Tredwell made 11 at number five before Ian Bell (21no) and Trott (7no) saw off the final overs.
Bangladesh had resumed on the day on 131 for three, with Roqibul and Ashraful at the crease.
Bresnan and Steven Finn probed well early on and the latter dismissed Roqibul when he had added just one to his overnight 50.
Finn, in the middle of a testing six-over spell that included five maidens, rocked back off stump having beaten the batsman for pace.
Ashraful looked in fluent form as he eased to 30 before Ajmal Shahzad coaxed one to stay low and shattered the stumps.
The hosts then crawled to 167 before Cook decided to abandon the pretence of a proper match and accelerate proceedings sufficiently to give his side two sessions in the middle.
Cook himself bore much of the shame, throwing down five overs of unadorned rubbish to close with scarcely believable figures of 5-0-111-0.
Carberry was his partner in crime, offering the batsmen a succession of slow long-hops that yielded 78 in four overs.
Shuvogoto Chowdury made a rapid 91no and Dollar Mahmud 66no, though neither man bothered to acknowledge their nominal half-centuries, before lunch brought the declaration on 362 for five.