  We give an alternative argument to the application of the so-called Maurey-
Nikishin-Pisier factorisation in Fourier restriction theory. Based on an
induction-on-scales argument, our comparably simple method applies to any
compact quadratic surface, in particular compact parts of the paraboloid and
the hyperbolic paraboloid. This is achieved by constructing near extremisers
with big "mass", which itself might be of interest.

Classical Analysis and ODEs