Safari 9 with Yosemite, serious cookie problem

I updated to Safari 9 while still on Yosemite, and now the cookies cannot be stopped - there seems to be a serious problem with the new Safari. Regardless of how I set the cookie policy under Safari > Preferences > Privacy, hundreds of cookies quickly accumulate (in a few minutes) and drive the CPU load very high. This is true even if I set Safari to "always block" cookies. If I remove all website data, the cookies just keep accumulating. Is there a good solution for fixing this? I never before experienced a cookie problem with version 8 of Safari.