As with any balancing act there was a certain amount of wobbling going on. In a newspaper article published yesterday morning, the Home Secretary assured his readers there was no problem with the Government's requirement that the courts distinguish between "serious violence" and "violence".
Some might think that deciding which was which was a rather subjective judgement but Mr Straw was confident the Bill "distinguishes more clearly than ever before" the circumstances in which anti- terrorist legislation would apply.
In the House though, where he knew he would have to brace himself for destabilising gusts from both sides, he seemed less confident. It was a "fine line", he conceded and, though he did not add this, fine lines are not conventionally associated with easy public consensus.
Presumably it is a very clear fine line. You need to do a bit of careful work with a magnifying glass to discern exactly where the line runs and then everything's dandy. Mild violence, modest violence, a broad band of middling violence and then, bang, we're into serious violence and it's time to call the Anti- Terrorist Squad.
What separates Mr Straw from his opponents on this matter is his grand confidence in the powers of magistrates and law enforcement agencies to make such distinctions. He is serenely confident the powers won't be abused, that the world will proceed in a benign and sagacious manner.
But there were worrying signs yesterday that clarity of mind on this matter is not that easily arrived at. The Conservatives certainly know where they stand - so firmly behind the Home Secretary in the battle against anarchy and disorder that they hope to make him look half-hearted, even though he's introducing the Bill. But they have their wobbles too.
When Mr Straw expressed the view that without the Prevention of Terrorism Act casualties over the years would have been much greater John Greenway, sitting on the Opposition front bench, shook his head sorrowfully. Then, noticing that Andrew Mackay, sitting next to him, was vigorously nodding in agreement, he seamlessly converted the motion into matching wag of approval.
After a sceptical intervention from Douglas Hogg, Mr Straw tried to clarify matters with another adjective. The courts would be quite capable of distinguishing "heinous crime" from the ordinary kind. This did not placate his Labour critics, Jeremy Corbyn and Kevin McNamara. "Is there a cash value put upon it?" the former asked.
"We have to legislate with words because that is all we have," replied Mr Straw, a little plaintively. But his colleagues continued to show an old-fashioned desire to know exactly what the words meant before they would sign on the dotted line.
Down in Committee Room 15 Gordon Brown was being personally terrorised by Michael Fallon, having been called before the Treasury Select Committee to answer questions about the Pre-Budget report. Mr Fallon wanted the Chancellor to acknowledge a statistic that suggested tax had risen over the course of the Government. Mr Brown was equally determined to ignore it.
This he did by clinging to Table B7, a useful statistical matrix that had clearly been carefully drafted to exclude the embarrassing figure. Was the statistic there or not?
For Mr Fallon it was as plain as print. He had the page in his hand.
For Mr Brown, referring to an identical sheet of paper, it was equally clear - it was not in the table. I can only assume that a very fine line was all that lay between these incompatible visions of the same document.