And measures in the older version designed to monitor yeshiva attendance, such as the introduction of fingerprint scanners, have been removed.
A revised clause now states that, rather than recruiting from yeshivas, the government will only conscript graduates of Charedi educational institutions, defined as those who studied at such institutions for at least two years between ages 14 and 18.
Likewise, the new bill also provides an age limit on the sanctions imposed on draft dodgers.
Those Charedim who fail to report for duty will be banned from getting a driver's license or from travelling abroad - but only until they are 23.
They will also be made ineligible to receive housing subsidies, tax credits, national insurance discounts, daycare subsidies and travel discounts.
These sanctions, though, will expire when they reach the age of exemption, 26.
The redrafted bill has been devised by Likud MK Boaz Bismuth, who replaced Yuli Edelstein after the latter was ousted from his committee role by his own party.
Edelstein was pushed out after refusing to compromise with the main Charedi parties, Shas and United Torah Judaism, leading to a series of resignations that almost collapsed Prime Minister Netanyahu's coalition.
