Why don't we negotiate with terrorist hostage takers?

Some have criticized the United States policy of not negotiating with terrorists and not paying for hostages. The policy has always made sense to me. If a terrorist knows they will get paid large sums of money (or be able to influence U.S. policy) for hostages they will just be encouraged to take more hostages. Here is a story which gives another reason not to pay off hostage takers.

BERLIN (Reuters) - Part of the ransom money alleged to have been paid by the German government to win the freedom of Iraq hostage Susanne Osthoff last month was found on Osthoff after her release, the German magazine Focus said on Saturday. Without citing its sources, Focus said officials at the German embassy in Baghdad had found several thousand U.S. dollars in the 43-year-old German archaeologist's clothes when she took a shower at the embassy shortly after being freed. The serial numbers on the bills matched those used by the government to pay off Osthoff's kidnappers.

Several of the people kidnapped over the last couple years have been sympathetic to the cause of the insurgency. It wouldn't surprise me in the least to find out that more than a couple of the "kidnappings" were staged and that the "hostage" was paid for playing a convincing and sympathetic hostage.