Lancashire 273 (Chanderpaul 117*) and 146 for 4 (Davies 79) lead Warwickshire 321 (Umeed 113, Trott 56, Patel 50) by 98 runs
Both were in the side the last time England played a Test series - December in India, though Hameed missed the final Test through injury - but, for various reasons, it seems neither will retain their place.
Haseeb Hameed has simply not scored enough runs. In 15 first-class innings this season, he has failed to make a 50 and only reached 25 three times. He's been out for a duck four times.
By the time the India series finished, it seemed unthinkable that Hameed would not be retained for England's next Test. But, whether it's a case of county bowlers learning how to bowl at him after a successful first season in the game, or whether he is struggling mentally with the new levels of expectation with which he is confronted, is hard to say. His balance at the crease might also be a factor; his movements certainly don't seem as sharp as they did in India with a prop onto the front foot perhaps leaving him exposed when he has to play back.
Butter was promoted to open in the second innings here. It was a tactical decision based upon the hope that he might enjoy the pace of the harder ball and also soften it more quickly. Worcestershire enjoyed success with similar tactics against Durham.
It was selfless of Buttler to agree to such a ploy. But whether it's what he needs at this stage of his career is debatable. Rather than bringing his undisputed white ball skills to play in red (or pink) ball cricket, he might be better served developing his long-form skills.
He hasn't had much chance to do that. Since the end of the 2014 season, he has played just two Championship games and scored 45 Championship runs. He has played 15 Tests, it is true, but few learn their trade at the top level without an apprenticeship. It is asking a lot of him to do so.
It would be understandable if Buttler didn't continue to pursue a future as a red ball player. He doesn't need to: his status as a white ball player - and his earning potential - is strong. If he helps England win a World Cup, he can retire with a proud record.
He has always said, however, that he is keen to make it as a Test player and he clearly has the raw ability to do so. But, as John Lennon put it, life is what happens to you while you're busy making other plans. And the down side of England's new prioritisation of white ball cricket - the decision to play in the IPL rather than County Championship; the decision to allocate a window in prime summer to a new-team T20 competition - is that there is simply no time for players like Buttler to learn their red-ball trade. It's no-one's fault, it's just a reflection of the modern world.
Anyway Buttler, having attempted a lavish swipe outside off stump, soon departed to a catch at mid-wicket as he tried to clip one through the leg side. And Hameed, who survived a strong leg before shout on 15, was then trapped by a little away swing as he shaped to play through mid-wicket and was beaten by one that looked as if it were heading on to his pads, but straightened towards middle and off.
Both might have learned a thing or two from Andy Umeed's innings. While both Hameed and Buttler paid for playing across the line, Umeed played resolutely straight and demonstrated remarkable patience in adding 100 for Warwickshire eighth-wicket with Jeetan Patel.
It has emerged - courtesy of Robert Brooke, co-founder of the Association of Cricket Statisticians and Historians - that Umeed's century was the second slowest (in terms of minutes; records in terms of balls have only been reliably kept since about 1987) in the history of the County Championship after Jason Gallian's 453 minute effort for Lancashire against Derbyshire at Blackpool in 1994. It took Umeed 429 minutes to reach three-figures, which was nine minutes slower than WH 'Billy' Denton's 420-minutes century for Northants against Derbyshire in 1914.
Warwickshire's management have been asking for their batsmen to show some fight for a few weeks; in Umeed they found an old-fashioned battler. It is not a fashionable quality, but then nor are good manners or driving on the inside lane on a motorway and those things have value, too.
The most fluent batting on day three of this game came from Alex Davies. Driving, cutting and pulling with more freedom than anyone else has managed all game, Davies helped Lancashire wipe off the first innings arrears of 48 and gain a lead of 130 going into the final day.
But when he fell top-edging an attempted pull and Steven Croft laced another pull to mid-wicket where Umeed took an excellent catch - it seems he can move pretty fast when required - Warwickshire clawed their way into the game once more. If the weather holds, we might yet have a terrific finish here.
George Dobell is a senior correspondent at ESPNcricinfo