  We consider a symmetric, finite-range contact process with two types of
infection; both have the same (supercritical) infection rate and heal at rate
1, but sites infected by Infection 1 are immune to Infection 2. We take the
initial configuration where sites in $(-\infty,0]$ have Infection 1 and sites
in $[1,\infty)$ have Infection 2, then consider the process $\rho_t$ defined as
the size of the interface area between the two infections at time $t$. We show
that the distribution of $\rho_t$ is tight, thus proving a conjecture posed by
Cox and Durrett in [Bernoulli 1 (1995) 343--370].
