One can understand the fears and doubts of many of us, both Jews and Arabs, regarding the extent to which the agreement to maintain calm will succeed. But the thought about the casualties that will probably be prevented by the very fact that there is an understanding about a cease-fire is enough to support the new process; moreover, many people believe that, this time, it's serious.

The process began with a Palestinian initiative. The Israeli prime minister did not have much choice nor did he have the option of refusing the proposal. After all, we have just emerged from one difficult war - can Israel continue to fight? And if it can, is it wise to do so when the president of the United States is in the region?

Nevertheless, this fact should not lead us to a conclusion which will minimize the value of the positive Israeli stance.

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The initiative was not that of Hamas, as various Israeli experts believe, but of Abu Mazen (Mahmoud Abbas). The chairman of the Palestinian Authority, who Israel and the West have decided is a weak leader, brought about a cease-fire as a result of a long and wise process of persuasion and pressure.

He conducted a public campaign against those who plan and carry out the firing of Qassam rockets on the communities of the western Negev; he spoke up against the shooting every day and at every opportunity, particularly in Arabic and in the Arab media - so the Palestinians and the Arabs would hear.

He called the firing despicable and accursed, and even mentioned the fact that many Qassams fell within the Gaza Strip itself and caused casualties among the Palestinians - a fact that is not discussed much either by Hamas or in Israel, for good reason.

Abu Mazen also held the rocket launchers fully responsible for the siege that is suffocating the Palestinian people, and spoke about the hungry families, the social decline and the destruction of families.

His words were an accurate expression of the innermost feelings of the Palestinian people. Without this public pressure it would not have been possible to bring the rocket launchers to a decision about a cease-fire.

It is not correct to think that everything was a staged maneuver and that Hamas planned the cease-fire in order to gain time and to become stronger. If it does in fact become stronger, that won't be related to the cease-fire.

Hamas, even abroad under the leadership of Khaled Meshal, came to a clear conclusion that if the situation continues as it has until now, Abu Mazen is liable to disperse the government and take steps to restore the decision to the people: In other words - to hold new elections. The surveys, including the internal ones by Hamas, leave no room for doubt that the Palestinian people will not vote for them again. They understood that if they want to continue to be the largest political power in the PA territories, they must cooperate in ending the siege.

The reaction of Prime Minister Ehud Olmert was also correct and realistic. It once again aroused hope on both sides, despite all the inevitable questions.

But that is not enough. We are only at the beginning of the process. Anyone who wants it to succeed must go forward with another brave decision: The extremists must not be allowed to determine our agenda. On both sides there are groups and streams that are not willing to accept the calm.

It is not important who they are and why they adopt this belief. They have always popped up on every day of quiet, and they always will.

The main thing is not to let them drag us after them, even if they succeed in spilling more blood.The conflict has exacted a high price from all of us. Every additional victim will be in vain.

On the other hand, there is a genuine opportunity to begin negotiations with the aim of achieving a solution to the conflict. The process will be long and difficult, but we must not be captives in the hands of those who do not believe in any solution and who have no plan other than war.