Recently, Simon and Wickramasekera (J Differ Geom 75:143-173, 2007) introduced a PDE method for producing examples of stable branched minimal immersions in ?~3. This method produces two-valued functions u over the punctured unit disk in so ?~2 that either u cannot be extended continuously across the origin, or G the two-valued graph of u is a C~(1,α) stable branched immersed minimal surface. The present work gives a more complete description of these two-valued graphs G in case a discontinuity does occur, and as a result, we produce more examples of C~(1,α) stable branched immersed minimal surfaces, with a certain evenness symmetry.
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