This is: Shanghaied in Tuscany!
Relais dell'Orologio, Pisa
The only independent hotel of the trip, the Relais dell'Orologio is nicely situated in a quiet side street, just a few minutes from the Piazza dei Miracoli. The hotel is a converted old manor house and it is worth bearing in mind the constraints that such a heritage imposes. Nevertheless, I found it comfortable and very well appointed, with an attractive courtyard restaurant at the rear. Like the majority of Trip Advisor reviewers, I did wonder about the justification for that fifth star, however.
On the face of it, this was a non-points earning stay. However I made the booking via the Expedia portal on bmi's website and as such, it should be good for a couple of thousand miles!