According to the brightness dependences on the cloudiness, identified in our previous studies of the artificial sky glow, we attempted a detailed examination of these relationships within the light island of Cracow. For this purpose we use the measurements made in one of the Cracow residential estate in conditions of a cloudless and overcast sky. We have also used the unique measurements made during a power failure on 25 August 2011. These measurements allowed us to separate the local and distant light pollution. This enabled the assessment of the contribution of these two types of light pollution into the total light pollution of the urban light-island. We also used our earlier year-round measurement series made in the same estate in Cracow as well as one of the neighboring villages, in order to determine the effect of the cloud genera on the distant light pollution.