A simple thermal-diffusive model for premixed flames with radiative heat losses is studied numerically. In accordance with previous analytical predictions, it is shown that cellular flames occurring in low Lewis number premixtures can propagate with heat-loss rates greater than the maximum that extinguishes the planar flame. At sufficiently high heat losses, the flame interface breaks up into separate caplike propagating flamelets while a significant portion of the fuel remains unconsumed. A further increase in heat losses leads to a total suppression of the flame.