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In an effort to better understand connectivity and capacity in wireless networks, the log-normal shadowing radio propagation model is used to capture radio irregularities and obstacles in the transmission path. Existing results indicate that log-normal shadowing results in higher connectivity and interference levels as shadowing (i.e., the radio irregularity) increases. In this paper we demonstrate that such a behavior is mainly caused by an unnatural bias of the log-normal shadowing radio propagation model that results in a larger transmission range as shadowing increases. To avoid this effect, we analyze connectivity and interference under log-normal shadowing using a normalization that compensates for the enlarged radio transmission range. Our analysis shows that log-normal shadowing still improves the connectivity of a wireless network and even reduces interference. We explain this behavior by studying in detail what network parameters are affected by shadowing. Our results indicate that, when it comes to connectivity and interference, an analysis based on a circular transmission range leads to worst case results.