  Following Gorkin, Mortini, and Nikolski, we say that an inner function $I$ in
$H^\infty$ of the unit disc has the WEP property if its modulus at a point $z$
is bounded from below by a function of the distance from $z$ to the zero set of
$I$. This is equivalent to a number of properties, and we establish some
consequences of this for $H^\infty/IH^\infty$.
  The bulk of the paper is devoted to "wepable" functions, i.e. those inner
functions which can be made WEP after multiplication by a suitable Blaschke
product. We prove that a closed subset $E$ of the unit circle is of finite
entropy (i.e. is a Beurling-Carleson set) if and only if any singular measure
supported on $E$ gives rise to a wepable singular inner function. As a
corollary, we see that singular measures which spread their mass too evenly
cannot give rise to wepable singular inner functions. Furthermore, we prove
that the stronger property of porosity of $E$ is equivalent to a stronger form
of wepability ("easy wepability") for the singular inner functions with support
in $E$.
  Finally, we find out the critical decay rate of masses of atomic measures
(with no restrictions on support) guaranteeing that the corresponding singular
inner functions are easily wepable.
