The government has rejected a call to ban masks and other face coverings at protests in the wake of violent student fee demonstrations in London.
Home Office Minister Lord Wallace said there was already legislation banning protesters from covering their face to conceal their identity.
But he told peers it should be up to police to decide when the law is used.
He said it would not be practical to have "snatch squads" of officers arresting masked demonstrators.
Police in some parts of the country have removed face masks from protesters at demonstrations by the English Defence League but the tactic has not so far been used at student tuition fee demonstrations.
The row comes as the Metropolitan Police released new images of people they want to trace in connection with last Thursday's violent protests in Parliament Square, some of whom had covered their faces making them harder to identify.
They have made 40 arrests so far, mostly on suspicion of violent disorder and criminal damage.
Conservative peer Baroness Miller called, in the House of Lords, on the government to ban masks at demonstrations.
She said: "It would be very helpful for the police if potential troublemakers were not wearing masks, which would allow them to move on potential troublemakers so that trouble was absolutely avoided."
But Lib Dem minister Lord Wallace said policing in Great Britain was by "consent" and the trust of the public had to be maintained.
He told peers: "It is a matter of judgement for the police whether someone who puts on a mask at a demonstration, in the middle of a very large crowd, should immediately be arrested."
He said he had been assured that some of the people arrested at the end of recent protests or days later had worn masks "during part of the demonstration", including those accused of vandalising a police van.
Former Metropolitan Police commissioner Lord Condon said it was an issue that required a "proportionate and balanced response and not an over-reaction".
Lord Wallace said the legal definition of a mask worn for the purposes of concealing identity and with the intention of committing violence was "tightly drawn" so that people trying to keep their face warm in cold weather or covering their face for religious reasons, such as wearing a burkha, could not be arrested.
He also assured peers that the police took seriously concerns about officers removing their identity badges to avoid potential prosecution.
Lord Trimble, former first minister of Northern Ireland, urged the minister to "think again" as the current law was so tightly drawn it made police officers "very cautious in their approach to things".
Wearing a mask in public had been illegal "for decades" in Northern Ireland and had not caused any problems, he claimed.
But Lord Wallace said it would not help "when police are trying to control a very large demonstration to ask for police snatch squads to try to go into the middle of the demonstration to try to seize particular protesters".