Entity disambiguation (ED) is the task of mapping an ambiguous entity mention to the corresponding entry in a structured knowledge base. Previous research showed that entity overshadowing is a significant challenge for existing ED models: when presented with an ambiguous entity mention, the models are much more likely to rank a more frequent yet less contextually relevant entity at the top. Here, we present NICE, an iterative approach that uses entity type information to leverage context and avoid over-relying on the frequency-based prior. Our experiments show that NICE achieves the best performance results on the overshadowed entities while still performing competitively on the frequent entities.