One of the primary tasks of morphological parsers is the disambiguation of\nhomographs. Particularly difficult are cases of unbalanced ambiguity, where one\nof the possible analyses is far more frequent than the others. In such cases,\nthere may not exist sufficient examples of the minority analyses in order to\nproperly evaluate performance, nor to train effective classifiers. In this\npaper we address the issue of unbalanced morphological ambiguities in Hebrew.\nWe offer a challenge set for Hebrew homographs -- the first of its kind --\ncontaining substantial attestation of each analysis of 21 Hebrew homographs. We\nshow that the current SOTA of Hebrew disambiguation performs poorly on cases of\nunbalanced ambiguity. Leveraging our new dataset, we achieve a new\nstate-of-the-art for all 21 words, improving the overall average F1 score from\n0.67 to 0.95. Our resulting annotated datasets are made publicly available for\nfurther research.\n