An income inequality measure satisfies the Pigou-Dalton transfer principle if progressive transfers decrease income inequality. When transfers cause transaction costs, one can trace out the maximum leakage such that the transfer pays at the margin. An income inequality measure is leaky-bucket consistent if the transaction costs of a transfer are neither negative nor do they exceed the amount of the transfer. We show that the Pigou-Dalton transfer principle and leakybucket consistency are not reconcilable. Experimental research has shown that subjects? behavior exhibit graded compensating justice, that is compensating income changes which maintain the degree of income inequality and point in the same direction should provide less income compensation for richer than for poorer income recipients. We also show that the Pigou-Dalton transfer principle and graded compensating justice are not reconcilable.