Clearly, they had learned a lesson from the unsavoury experience of the Agra summit.
The meeting was surrounded by a lot of media speculation, which drastically limited for the negotiators the manoeuvrability space that is so essential to the sorting out of such complex issues as the ones that have kept Pakistan and India in a perpetual state of confrontation for more than five decades.
This time, however, a great deal of preparatory work preceded the meeting between the two leaders, and care was taken not to reveal much information about the goings-on.
Secrecy has its own hazards. In the present case it led to all kinds of rumours and suspicions.
Many on the Indian side used the situation to indulge in wishful thinking and proclaim that Pakistan was ready to accept the LoC in Kashmir as a permanent border, even though only a few days earlier Vajpayee had told an interviewer from India Today that solution would not be acceptable to Pakistan.
Ordinary Pakistanis were bewildered by a number of drastic concessions that Pakistan had made to India within the framework of SAARC without a visible quid pro quo from the other side, prompting some to make noises about a sell-out.
It was to clear the atmosphere of such suspicions that the two sides decided to issue an unplanned joint communiqué.
President Musharraf also held a press conference on Tuesday where he declared, "History has been made", and further that the two sides had this time reached "where we had never reached in the past."
The communiqué was more explicit in acknowledging the need to resolve issues of primary concern to both sides.
Addressing the issue of principal importance to India, it said, "President Musharraf reassured Prime Minister Vajpayee that he would not permit any territory under Pakistan's control to be used to support terrorism in any manner."
This, in fact, is not the first time that the Pakistan President has held out the same assurance. He has been repeatedly saying that his country opposes terrorism in all its forms and manifestations, and that he would not allow Pakistani territory to be used for terrorism against 'any country'.
However, what is more significant in the present context is a meeting that took place during the recent days between the ISI chief and Indian officials.
Apparently, more concrete assurances were sought and furnished at that meeting.
While disclosing that the two sides had agreed to commence composite dialogue in February 2004, the joint communiqué said, "The two leaders are confident that the resumption of the composite dialogue will lead to peaceful settlement of all bilateral issues, including Jammu and Kashmir, to the satisfaction of both sides."
The last ten words in this statement indicate a historic change in the Indian stance. On closer examination, they reveal that it is for the first time ever that India has effectively dropped its 'integral part' refrain regarding Kashmir.
When it recognises that the Kashmir problem needs to be settled "to the satisfaction of both sides" it concedes two important points: one, that Kashmir is a disputed territory; and two, that India is willing to step back from its long stated position since it now seeks to settle the issue in a way that would be satisfactory for Pakistan as well. Indeed President Musharraf had good reason to express the optimism that he did when he told a press conference that "history has been made".
In fact it is not only President Musharraf and his colleagues in government who are painting a bright picture of things to come.
Significantly, the Kashmir hard-liners in this country too have been critical, it appears, but for the sake of criticism only.
Also, the leaders of both the factions of the All Parties Hurriyat Conference have welcomed the Musharraf-Vajpayee meeting and the ensuing agreement.
All of this shows that the Islamabad meeting has led to substantial progress on Kashmir, the main issue of contention between Pakistan and India.
Given that the next meeting is scheduled for as early as February, and much of the preparatory work has already been done, unless some unforeseen calamity strikes, the process may not take long to usher in a new era of peace and progress in the Subcontinent.
Information Minister Sheikh Rashid Ahmad has been talking of a two to three years' timeframe for the successful culmination of the peace process. One hopes it will turn out to be a valid forecast.