For two functions $f$ and $g$, define $g\ll f$ to mean that $g$ satisfies
every algebraic differential equation over the constants satisfied by $f$.
The order $\ll$ was introduced in one of a set of problems on algebraic
differential equations given by the late Lee Rubel. Here we characterise
the set of $g$ such that $g\ll f$, when $f$ is a given Liouvillian function.