Place egg yolk in a deep bowl or into a blender or food processor. Mix in cayenne, mustard and sugar. Stir in egg yolk and then add vinegar, lemon juice and a drop or tow of oil. Beat with fork or blend until thoroughly mixed. Continue adding the oil, a few drops at a time, beating vigorously or blending after each addition until about 1/4 of the oil has been used. A wire whisk is wonderful for making mayonnaise. Beat in the remaining oil, 1 or 2 tablespoons at a time. Mayonnaise thickens as it stands, but if too thick, it will separate on standing. Store in a covered jar in refrigerator or cool place. Lasts a few days. 

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