  A matrix is \emph{simple} if it is a (0,1)-matrix and there are no repeated
columns. Given a (0,1)-matrix $F$, we say a matrix $A$ has $F$ as a
\emph{configuration}, denoted $F\prec A$, if there is a submatrix of $A$ which
is a row and column permutation of $F$. Let $|A|$ denote the number of columns
of $A$. Let $\mathcal{F}$ be a family of matrices. We define the extremal
function $\text{forb}(m, \mathcal{F}) = \max\{|A|\colon A \text{ is an
}m-\text{rowed simple matrix and has no configuration } F\in\mathcal{F}\}$. We
consider pairs $\mathcal{F}=\{F_1,F_2\}$ such that $F_1$ and $F_2$ have no
common extremal construction and derive that individually each $\text{forb}(m,
F_i)$ has greater asymptotic growth than $\text{forb}(m, \mathcal{F})$,
extending research started by Anstee and Koch.
