Furthermore, smartphones are theoretically better PIMs than PDAs were because of their wireless connectivity.
Home Office minister Lord Henley pointed out that T-Pims would be subject to review by the courts.
The government has published draft proposals for "enhanced T-Pims", which are more restrictive.
BBC: New terror laws could be less effective, warns watchdog
Lord Lloyd argued, however, that T-Pims should be imposed according to "the balance of probabilities", which is used in civil law.
Renewing T-Pims legislation every five years "strikes the right balance", he said, adding that there were "other means by which the bill can be amended or repealed".
Lord Lloyd of Berwick, a crossbencher and former judge, opened the debate on 19 October 2011 by introducing a set of amendments targeting two key aspects of T-Pims.
Mrs May told the Commons that T-Pims would be "more focused and targeted" than the control orders regime set up under Labour, which was "neither perfect nor entirely effective".
T-Pims will have a maximum time-limit of two years, after which further measures can only be imposed on an individual if there is evidence of further engagement in terrorism.
Former Director of Public Prosecutions Lord Macdonald, a Liberal Democrat peer who oversaw the government's wider review of terrorism legislation, said the T-Pims, as they are known, were "an improvement on what went before".
In a Commons statement on 26 January 2011, Home Secretary Theresa May said that the existing control order regime will remain in place while the replacement "Terrorism Prevention and Investigation Measures", or T-Pims, are set up.
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