Only X-ray-bright superbubbles have been reported in the past. ROSAT provides an excellent opportunity to study X-ray-dim superbubbles. We have analyzed the ROSAT Position Sensitive Proportional Counter observations of four superbubbles in the Large Magellanic Cloud-DEM 31, DEM 105, DEM 106, and DEM 137. None of the four is detected at more than the 2 sigma level. The observed luminosities and the 3 sigma upper limits are consistent with the luminosities expected from energy-conserving bubbles, These results confirm that not all superbubbles are X-ray bright, suggesting that an intermittent process such as hidden supernova remnants is responsible for the X-ray-bright superbubbles.