Mammalian sperm show an unusual and heavily compacted genomic packaging state. In addition to its role in organizing the compact and hydrodynamic sperm head, it has been proposed that sperm chromatin architecture helps to program gene expression in the early embryo. Scores of genome-wide surveys in sperm have reported patterns of chromatin accessibility, nucleosome localization, histone modification, and chromosome folding. Here, we revisit these studies in light of recent reports that sperm obtained from the mouse epididymis are contaminated with low levels of cell-free chromatin. In the absence of proper sperm lysis, we readily recapitulate multiple prominent genome-wide surveys of sperm chromatin, suggesting that these profiles primarily reflect contaminating cell-free chromatin. Removal of cell-free DNA, and appropriate lysis conditions, are together required to reveal a sperm chromatin state distinct from most previous reports. Using ATAC-seq to explore relatively accessible genomic loci, we identify a landscape of open loci associated with early development and transcriptional control. Histone modification and chromosome folding profiles also strongly support the hypothesis that prior studies suffer from contamination, but technical challenges associated with reliably preserving the architecture of the compacted sperm head prevent us from confidently assaying true localization patterns for these epigenetic marks. Together, our studies show that our knowledge of chromosome packaging in mammalian sperm remains largely incomplete, and motivate future efforts to more accurately characterize genome organization in mature sperm.