  For a Banach space $X$ with a shrinking Schauder frame $(x_i,f_i)$ we provide
an explicit method for constructing a shrinking associated basis. In the case
that the minimal associated basis is not shrinking, we prove that every
shrinking associated basis of $(x_i,f_i)$ dominates an uncountable family of
incomparable shrinking associated bases of $(x_i,f_i)$. By adapting a
construction of Pe{\l}czy{\'n}ski, we characterize spaces with shrinking
Schauder frames as spaces having the $w^*$-bounded approximation property.
