This paper is a continuation of [V. Jiménez López, An explicit description of all scrambled sets of weakly unimodal functions of type 2∞, Real Anal. Exchange, to appear.], where a explicit description of the scrambled sets of weakly unimodal functions of type 2∞ was given. Its aim is to show that, for an appropriate non-trivial subset of the above family of functions, this description can be made in a much more effective and informative way