We consider the problem of estimating the common mean of univariatedata, when independent samples are drawn from non-identical symmetric,unimodal distributions. This captures the setting where all samplesare Gaussian with different unknown variances. We propose an estimatorthat adapts to the level of heterogeneity in the data, achievingnear-optimality in both the i.i.d. setting and some heterogeneoussettings, where the fraction of "low-noise" points is as small as logn. Our estimator n is a hybrid of the modal interval, shorth, andmedian estimators from classical statistics. The rates depend on thepercentile of the mixture distribution, making our estimators usefuleven for distributions with infinite variance.