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Definitely agree with that.. and whatever you do, don't delete it!

The rule of thumb is a 301 redirect passes 90-99% of page rank. If the 301 is redirecting to another page on the same domain, it's probably closer to 99%. I would not worry about the 1% loss.

Redirecting to https on the same domain actually improves page rank. Google likes HTTPS, and it is a positive ranking factor.

Can you describe your more detailed search in more detail? I also noticed that Moz misses a lot of backlinks

Hi, we are trying to move all of our website content from www.mysite.com to a subdomain (i.e. content.mysite.com), and make "www.mysite.com" nothing more than an iFrame displaying the content from content.mysite.com.

We have about 10 pages linking from the home page, all indexed separately, so I understand we'll have to do this for every one of them. (www.mysite.com/contact will be an iframe containing the content from content.mysite.com/contact, and we'll need to do this for every page)

How do we do this so Google continues to index the content hosted at content.mysite.com with the parent page in organic results (www.mysite.com). We want all users to enter the site through www.mysite.com or www.mysite.com/xxxxxx, which will contain no content except for iFrames pulling in content from content.mysite.com. Our fear is that google will start directing users directly to content.mysite.com, rather than continue feeding to www.mysite.com.

If we use www1.mysite.com or www2.mysite.com as the location of the content, instead of say content.mysite.com, would these subdomain names work better for passing credit for the iFramed content to the parent page (www.mysite.com)?

Thanks!

SIDE NOTE:  Before someone asks why we need to do this, the content on mysite.com ranks very well, but site has a huge bounce rate due to a poorly designed CMS serving the content. The CMS does not load the page in pieces (like most pages load), but instead presents the visitor with a 100% blank page while the page loads in the background for about 5-10 seconds, and then boom 100% of the page shows up. We've been back and forth with our CMS provider about doing something about this for 5 years now, and we have given up. We tested moving our adwords links to xyz.mysite.com, where users are immediately shown a loading indicator, with our site (www.mysite.com) behind it in an iFrame. The immediate result was resounding success... our bounce rate PLUMMETED, and the root domain www.mysite.com saw a huge boost in search results. Problem with this is our site still comes up in organic results as www.mysite.com, which does not have any kind of spinning disk loading indicator, and still has a very high bounce rate.