Identifying binding sites of transcription factors (TFs) is a key task in deciphering transcriptional regulation. ChIP-based methods are used to survey the genomic locations of a single TF in each experiment. But methods combining DNase digestion data with TF binding specificity information could potentially be used to survey the locations of many TFs in the same experiment, provided such methods permit reasonable levels of sensitivity and specificity. Here, we present a simple such method that outperforms a leading recent method, centipede, marginally in human but dramatically in yeast (average auROC across 20 TFs increases from 74% to 94%). Our method is based on logistic regression and thus benefits from supervision, but we show that partially and completely unsupervised variants perform nearly as well. Because the number of parameters in our method is at least an order of magnitude smaller than CENTIPEDE, we dub it MILLIPEDE.