Rolling out shortly (currently in beta so talk to your Google rep) is Remarketing Lists for Search
It gives the option of combining existing remarketing lists with your Search ad campaigns. This gives you two main options.
Only show ads to people searching for the specified keywords IF they are already on the remarketing list.
In other words show ads to the intersection of those two groups of people – those people who already ‘know, like & trust’ you.
Or you can choose to use the remarketing list as an exclusion list.
And only show ads to people searching for your keywords who are NOT already on the remarketing list.
ie only show ads to ‘new’ prospects.
Of course you can still choose the length of the ‘membership duration’ that you combine with your search campaigns, so ensure that multiple options are tested. Results will vary.
Try both options, just remember that you’ll need different marketing messages for those two very different groups of people.