We argue that while fluctuating fronts propagating into an unstable stateshould be in the standard KPZ universality class when they are {\em pushed},they should not when they are {\em pulled}: The universal $1/t$ velocityrelaxation of deterministic pulled fronts makes it unlikely that the KPZequation is the appropriate effective long-wavelength low-frequency theory inthis regime. Simulations in 2$D$ confirm the proposed scenario, and yieldexponents $\beta \approx 0.29\pm 0.01$, $\zeta \approx 0.40\pm 0.02$ forfluctuating pulled fronts, instead of the KPZ values $\beta=1/3$, $\zeta =1/2$. Our value of $\beta$ is consistent with an earlier result of Riordan {\emet al.}
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