Inner Functions satisfying the Weak Embedding Property (WEP) were introduced by Gorkin, Mortini and Nikolski in 2008 in relation to the Corona Theorem and Invertibility problems in Quotient Algebras. The WEP can be understood as a weak version of the classical Carleson Embedding Property. An inner function is called Wepable if there exists another inner function whose product satisfies the WEP. We will study the entropy and porosity of the support set of Wepable singular inner functions. The new results in the talk are joint work with A. Borichev and P. Thomas.