There is a cousin to the easyout called a nipple extractor. They are shorter and fatter, and made to grip the inside of pipe. The set I linked goes down to 1/8 inch pipe, which is a common size for grease zerks.
Husky's pipe nipple extractor set removes broken or frozen pipe nipples with ease. The extractors feature a durable, heavy-duty hardened steel construction and can accommodate 1/8 in., 1/4 in., 3/8 in.,