  We consider the KPZ equation in $1$ spatial dimension with noise that is
rougher than white by an exponent $\gamma>1/4$. Under a weak coupling limit,
formally removing the nonlinearity from the equation, we show using regularity
structures that the renormalised solutions converge to a Gaussian limit that is
different from the solution of the linear part of the equation. The regime of
this effect has a nontrivial overlap with the subcritical regime $\gamma<1/2$.
