Mr Bundy began by noting that in the Pedra Branca case, Malaysia had argued in its written pleadings that notices to mariners, that is, ship captains, are irrelevant for questions of sovereignty.
That was in reference to a notice issued by the Governor of the Straits Settlements to inform mariners that a lighthouse had been built on Pedra Branca.
In the Sipadan and Ligatan case, however, Malaysia had relied on the building and notification to mariners of unmanned lights on the two islands. It argued then that was a 'straightforward reflection' of its sovereignty.
'Consistency,' Mr Bundy told the court yesterday, 'appears to have its limits for Malaysia when territorial questions are at issue.'
Another international lawyer on the Singapore team, Professor Alain Pellet, also pointed to inconsistencies in Malaysia's other arguments.
For example, Malaysia first claimed that the numerous examples that Singapore cited as displays of sovereignty were not, in fact, state activities.
These acts included Singapore's naval patrols and investigations of shipwrecks that occurred in the waters around Pedra Branca.
But after Malaysia laid claim to the island in 1979, it tried to 'back up its reasoning', Prof Pellet said, by protesting against these very same acts.
In 2003, Malaysia protested for the first time against Singapore's naval patrols in the area, which had been going on since 1975 when the Singapore navy was formed.
The sovereignty dispute began when Malaysia first laid claim to the island in 1979, by publishing a map that placed Pedra Branca within its territorial waters.
Singapore promptly challenged the claim.
Singapore's lawyers also noted that the ICJ had stated in the Sipadan and Ligatan case that acts which took place after a dispute arose would be considered only if they were a normal continuation of prior acts and not undertaken to improve the legal position of the party relying on them.
Mr Bundy stressed that with respect to Pedra Branca, Singapore's conduct 'did not change one bit' after Malaysia's 'belated claim' emerged in 1979.
It simply continued to administer the island as part of its territory, as it always had, he said.
Mr Bundy also laid out in detail the numerous acts, including the passing of laws relating to Pedra Branca, that attested to Singapore's longstanding sovereignty over it, dating back to 1847.
The evidence also showed that Malaysians themselves recognised that Singapore owned and controlled the island.
Mr Bundy told the court that in March 1974, a number of Malaysian officials sought permission from Singapore to visit Pedra Branca to carry out tidal surveys.
Singapore asked for the names, passport numbers and details of their intended length of stay, which were provided to it by an officer of the Malaysian navy.
A second incident took place in 1978, when two officials from the Malaysian Survey Department arrived unannounced on Pedra Branca.
They were told by the Singapore lighthouse keeper that they could not stay without prior permission from the Port of Singapore Authority.
The hearing continues today. Deputy Prime Minister and Law Minister S. Jayakumar will wrap up Singapore's presentation, before the court resumes on Tuesday to hear Malaysia's case.