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I am not a great expert having only done that a number of times and the last 2 times I did not worry about it much ..
I think if you want the least reduction before you get improvements that you will have built in to come through then I would try to make sure that all the existing pages still return a page when polled by the robots.
Even if they will not have a correspondingly named page in the new site.
So if there are pages from the old site that will become deleted / orphaned, you have a choice, you could add links (to the new pages) and a message to them to take people (and robots) to the new site or could change them into mainly redirect pages (manual rather than autoredirecting). If you remove the content from them in the first instance then they may loose rank for their terms so I would be tempted to add a text and link ..
This page is being depreciated in favour of our new site, click this link to visit the new site.
leave the rest of the old page as is to keep some content on the page until the new site is fully indexed and visitors get to find the new pages in the engines.
Then you could replace / delete the old pages leaving a 404 and custom 404 redirect solution so that anyone still arriving to old page addresses is brought into the new site as soon as possible.
Hope that helps and if anyone else knows any better tricks, I will be interested to read them also.
It will take a bit more work but will be a lot more solid, and in the end you have double the value to bootstrap the next site.
Today, I can create instant PR5 pages within 30 days. Soon I'll be able to create instant PR6 pages without any other help. You get the idea.
SN