Abstract: We present a truly simple analysis of k-means|| (Bahmani et al., PVLDB 2012) -- a distributed variant of the k-means++ algorithm (Arthur and Vassilvitskii, SODA 2007) -- and improve its round complexity from O(log (Var X)), where Var X is the variance of the input data set, to O(log (Var X) / log log (Var X)), which we show to be tight.