iCloud freezes Mail

I've been in despair about Mail freezing on launch, about three times out of four. I have to force quit and try to launch again. Sometimes I have to launch-force quit-launch as many as six or seven times just to get my email. Once Mail launches, it works reliably. This has been going on for months, through at least one or two upgrades of Yosemite. (I'm on a brand new Mac Mini with Yosemite 10.10.4).

Mail also freezes on launch on my Macbook, also with the current version of Yosemite, though not as often.

Today I spent some time trying to isolate the problem. I used a criterion of six consecutive successful launches. Started with Mail-->Preferences-->Rules. I turned off all the rules -- I have more than twenty rules. (The rules are for filtering messages, routing them to various mailboxes.) This did not solve the problem.

Then I looked at System Preference --> Internet Accounts. A few at a time, I un-checked "enable this account" for POP accounts, tried to launch, and so on. No help. Then I turned off "Mail" for IMAP accounts, a few at a time. I isolated one problem account. To my surprise, that turned out to be the Mail portion of iCloud. That was the one I assumed would NOT be the problem. After all, Apple makes both Mail and iCloud.

I've isolated the problem on both machines. Turn off Internet Accounts --> iCloud -- > Mail, and Mail launches every time. Turn it back on, and Mail frequently freezes on launch.

This makes me pretty mad. I've sent hundreds of force-quit reports to Apple in the past six months. They must know about this.

Does anyone know why this happens and how it can be remedied? Thanks in advance.