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The weak boundedness property associated with a standard alpha-fractionalCalderon-Zygmund operator and a weight pair is good-lambda controlled by thetesting conditions and the Muckenhoupt and energy side conditions. As aconsequence, assuming the side conditions, we can eliminate the weakboundedness property from Theorem 1 of arXiv:1603.04332v2 to obtain that T isbounded if and only if the testing conditions hold for T and its dual (anearlier instance of this type of conclusion appears in Lacey and WickarXiv:1312.6163v3). As a corollary we give a simple derivation of a two weightaccretive global Tb theorem from a related T1 theorem. The role of twodifferent parameterizations of the family of dyadic grids, by scale and bytranslation, is highlighted in simultaneously exploiting both goodness and NTVsurgery with families of grids that are common to both measures.

A Good-Lambda Lemma, two weight T1 theorems without weak boundedness, and a two weight accretive global Tb theorem