This article is the second in a series that deals with the viscoelastic properties of Hot-melt pressure-sensitive adhesives (HMPSAs) based on formulations of block copolymers and tackifying resins. The viscoelastic properties of HMPSAs govern, to a large extent, their adhesion, processing, and end-use properties. In the first part of this article, we present a brief description of the rheological behavior of styrene isoprene styrene-styrene isoprene [SIS-SI] copolymer blends at room temperature. We then present an original approach that may lead to the design of new block copolymers (tetrablock and radial copolymers) that mimic the rheological behavior at room temperature of optimized SIS-SI blends used in adhesive formulations. We describe the concept and calculations that lead to the design of the characteristics of these new molecules. In the third part of this article, we discuss in detail the rheological behavior of these new block copolymers compared with the observed behavior of equivalent SIS-SI. In the last part we also demonstrate how the molecular model of the rheological behavior developed in the first article of this series can be applied to these new molecules. We propose, in particular, to apply the blending law (presented in the first article) on the complex shear modulus instead of the relaxation modulus, which simplifies calculations and even leads to a better agreement with experimental data. As a conclusion, we show how this original approach can bring really innovative solutions for the formulation of adhesives with specific properties by using molecular concepts of viscoelasticity.