In certain cases, the following IIS configuration must be changed so that the verbs PUT and DELETE are accepted: in IIS Manager, access "Handler Mappings" and then edit the "ExtensionlessUrlHandler-Integrated-4.0". Access "Request Restrictions", click the "Verbs" tab, and add the verbs "PUT,DELETE". Note that there can be no spaces between the verbs.
Also note that IIS must be restarted after this modification.