Using Pageant with TortoiseGit with two accounts - need to keep deleting SSH keys

I have access to two BitBucket accounts. I want to use SSH for both of them. I'm using TortoiseGit and Pageant for authentication.

However, I have to keep removing the SSH keys from Pageant to be authenticated correctly. This is what I have to do at the moment:

1. Delete all the keys from Pageant.
2. Do operation on repository in account A. Successful.
3. Do operation on repository in account B. Successful.
4. Attempt operation on repository in account A. Get a "conq : repository access denied" message until I delete the key for the other account from Pageant.

How can I get this to work properly? I've Googled and found stuff about ~/.ssh/config but I'm pretty sure that's a Linux thing. I've also found mention of using "sessions" in Putty.exe, but it seems I can only use the host name to select what session I want to use - as both accounts are with bitbucket.org I don't think that'll work.

Any help would be appreciated. Really can't understand why this is so complicated!

Explanation and workaround for Putty can be found here:

https://answers.atlassian.com/questions/150285/only-the-top-listed-private-key-in-pageant-is-used-offered-by-git-sourcetree-tortoisegit