England will look to take the first Test out of the West Indies' grasp on day four in Antigua, after Gary Ballance and Joe Root took their lead past 200.
The tourists ended the third evening 220 in front at 116 for three, thanks in large part to a made-in-Yorkshire stand of 64 between Balance (44no) and Root (32no).
England already held a first-innings advantage of 104 but set out shakily when some expert new-ball pressure took out Jonathan Trott, Alastair Cook and Ian Bell cheaply.
The fourth-wicket pair probably did enough to render a home win extremely unlikely and the focus now turns to the size of the chase they will leave.
Spinner James Tredwell, who chimed in with four for 47 on his first Test appearance in five years, was in confident mood.
"To get that partnership and take the lead over 200 puts us in a reasonable position," he said.
"It was certainly an important stand for us at the end, it could have gone the other way quite easily because they bowled pretty well at the top.
"If we can build that partnership first thing, or another one soon after, that's when the scoring rate can increase and give us more time to bowl them out.
"That's what we will be focusing on."
As for Tredwell, he reacted to news of fellow spinner Moeen Ali's imminent arrival in the Caribbean in the best possible manner.
He would probably have been playing drinks waiter had Moeen been available to start the tour, but was instead handed a second cap in five years.
Moeen will present an attractive option if passed fit on arrival in Grenada on Saturday, but the combination of Tredwell's efforts and Trott's unconvincing return at opener could force a rejig.
Moeen heads the innings in white-ball cricket and with Trott scoring six runs in his last four innings on tour, that might prove the likeliest vacancy.
Asked whether the all-rounder's summons affected his own position, Tredwell said: "It's probably at the back of my mind but you try not to think too deeply about that.
"I wanted to give them a bit of a headache, shall we say, and hopefully I've done that now.
"So it's over to the people who matter to make that decision going forward in the series. There's another important innings to come so hopefully we can knock them over and get the win."
Elsewhere there was a second critique of Cook's technique in three days from the West Indies camp.
Forty-eight hours after Kemar Roach declared he had a weakness that was common knowledge, centurion Jermaine Blackwood had his own thoughts on the touring skipper.
"Alastair always drives so we were trying to drag his hands away from his body and Jerome Taylor did that very well," he said.
"He was bowling to a plan. Taylor always sticks to a plan and when it works you celebrate."
Source: PA
