Conservative officials have approved rules for the party leadership contest to squeeze out outsider candidates early in the race.
Hopefuls including Esther McVey, Rory Stewart and Andrea Leadsom could all be at risk under new rules designed to streamline the process and bring it to a swift conclusion.
In a joint statement from the 1922 committee and Conservative Party board on Wednesday night, the new rules were confirmed.
The leadership contest works by MPs backing contenders in a series of ballots until the candidates are whittled down to two who then face a vote of Tory members.
At the first ballot, MPs hoping to succeed Theresa May with 16 MPs or fewer backing them will be eliminated. At the second ballot, the threshold has been raised to 32 or fewer.
McVey, Leadsom and Stewart have just a handful of MPs behind them, according to Conservative Home, while Health Secretary Matt Hancock has 11.
Boris Johnson, Dominic Raab, Jeremy Hunt, Sajid Javid and Michael Gove would appear to have enough support.
The rule change will pile pressure on candidates with a small pool of support to pull out.
It comes as Kit Malthouse and James Cleverly confirmed they had abandoned the contest on Wednesday.
The closing date for nominations is Monday June 10. The first ballot will take place on Thursday June 13, with further ballots scheduled on June 18, 19 and 20.