  The famous theorem by Chomsky and Sch\"utzenberger (CST) says that every
context-free language $L$ over an alphabet $\Sigma$ is representable as $h(D
\cap R)$, where $D$ is a Dyck language over a set $\Omega$ of brackets, $R$ is
a local language and $h$ is an alphabetic homomorphism that erases unboundedly
many symbols. Berstel found that the number of erasures can be linearly limited
if the grammar is in Greibach normal form; Berstel and Boasson (and later,
independently, Okhotin) proved a non-erasing variant of CST for grammars in
Double Greibach Normal Form. In all these CST statements, however, the size of
the Dyck alphabet $\Omega$ depends on the grammar size for $L$. In the Stanley
variant of the CST, $|\Omega|$ only depends on $|\Sigma|$ and not on the
grammar, but the homomorphism erases many more symbols than in the other
versions of CST; also, the regular language $R$ is strictly locally testable
but not local. We prove a new version of CST which combines both features of
being non-erasing and of using a grammar-independent alphabet. In our
construction, $|\Omega|$ is polynomial in $|\Sigma|$, namely
$O(|\Sigma|^{46})$, and the regular language $R$ is strictly locally testable.
Using a recent generalization of Medvedev's homomorphic characterization of
regular languages, we prove that the degree in the polynomial dependence of
$|\Omega|$ on $|\Sigma|$ may be reduced to just 2 in the case of linear
grammars in Double Greibach Normal Form.
