We simulate 3-flavour lattice QCD at finite temperature and isospin chemicalpotential $\mu_I$. In particular we study the nature of the finite temperaturetransition for quark masses close to the critical mass at which this transitionfor zero chemical potentials changes from a first order transition to acrossover. We find that the Binder cumulants, used to determine the position ofthis transition, have very strong dt dependence. This leads us to an estimateof the critical mass which is about 20% below previous estimates. In addition,when this dt dependence is taken into account, we find that the Bindercumulants show very little dependence on mu_I. From this we conclude that we donot as yet see any evidence for the expected critical endpoint. We have arguedpreviously that the position and nature of the finite temperature transitionfor small mu_I should be the same as that for small quark-number chemicalpotential mu.
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