Clustering pixels based on learned instance-discriminative pixel embeddings is a promising approach for the instance segmentation task, particularly with highly cluttered objects. The pixel embedding space is typically trained with proxy-based losses due to the large number of pixel samples. However, we have found that training guided by randomly sampled pixel triplets is not only feasible but also consistently yields better results. With our proposed loss, a basic convolution-based model achieves state-of-the-art results, with minimal pre- and post-processing, on a variety of biomedical datasets: FluoDSB (fluorescence cell), CVPPP (Arabidopsis leaf), Celegans (C. elegans nematode), and Neuroblastoma (cultured neuroblastoma cell).