Mr Straw claimed the measure appeared to allow by the back door judicial discretion over sentencing, while minimum sentences for repeat burglars and drug-dealers could be reduced by a fifth where the defendant pleaded guilty.
The impact of the two provisions can only be accurately gauged once judges begin to implement the new law, however, and are unlikely to prevent a rebellion in the Lords.
But they might make it easier for Labour to give its support, however grudging, to the changes.
Under the Home Secretary's original proposals, there was to be a rigid regime for automatic indeterminate life sentences for twice-convicted sex or violent offenders, and mandatory minimum jail terms for third-time burglars and hard-drug dealers.
But by April this year, he had conceded exceptions "only for exceptional circumstances". The Bill now says the sentences will be imposed "unless the court is of the opinion that there are exceptional circumstances which justify its not doing so".
Critics argued that the proposals would mean fewer not-guilty pleas and plea bargains, clogged courts, more pressure for victims and the risk of wrongful acquittals of the guilty.
Implementation of the changes to the prisons system will be staggered. In an interview with The Independent, Richard Tilt, director-general of the Prison Service, says the jail population would rise by less than 100 in the first year.Reuse content