Implications of the conjecture that the solar corona is heated by small-scale events (nanoflares) are examined. It is shown that even if these nanoflares are small-scale (heating areas much smaller than 1 arc sec2) and impulsive, the corona may still be rather homogeneous. In particular, the filling factor (defined as the ratio of the coronal volume radiating in X-rays and EUV to the total volume) can easily be of order unity. Future experimental determination of the filling factor could prove useful in estimating the volume of coronal material that is heated during nanoflares.