Hello, I need some (a lot of) help with this:

(a) If what you want to say that a private agreement has been signed on a specific date and place, meaning it is a private agreement between the parties that have signed on that day and place, would you say:
-"...private agreement signed on xxxx, in..."
-..."private signed agreement on xxx, in..."

(b) If you don't make reference to the date or place, and you just want to state the fact that the signed agreement was private, meaning that it is only binding to the parties that have signed it, would you say:
-"...private signed agreement..."
-"...the signed private agreement..."
-"...the private agreement signed..."
-"...the agreement under private signatures..."
or what???
(Am I making any sense?)
Thank you!