Sheffield United's target is to make Premier League 'mini-league' bigger and spread the nervousness
But any win will make those higher up squirm a little more, and the Blades hope to start that with victory at Brighton and Hove Albion on Sunday.
"That’s our intention to do that," said Heckingbottom ahead of the game. "Imagine if we get a couple more wins and what teams will then be thinking?
"We want it as tough as possible and I would think the other teams at the bottom would want that.
"We don’t just want four teams at the bottom. You want to get as many wins as possible and as early as possible for two reasons.
"You want to be out of trouble, of course you do, but you want as many people as possible in a dogfight with you.
"Let them feel the pressure as well."
Regardless of the bigger picture, though, the Blades' task remains the same – accumulating as many points as possible. So far they only have four with 11 games played, a ratio they will have to improve to secure Premier League safety.
"Our focus won’t change unless we’re winning the next dozen games and we’re in a totally different position in the league," said Heckingbottom.
"Our goal is still going to be the same.
"We want more points to drag even more teams into it.
"The sooner we can do that the better."