In cancer metastasis and other physiological processes, cells migrate through the three-dimensional (3D) extracellular matrix of connective tissue and must overcome the steric hindrance posed by pores that are smaller than the cells. It is currently assumed that low cell stiffness promotes cell migration through confined spaces, but other factors such as adhesion and traction forces may be equally important. To study 3D migration under confinement in a stiff (1.77 MPa) environment, we use soft lithography to fabricate polydimethylsiloxane (PDMS) devices consisting of linear channel segments with 20 μm length, 3.7 μm height, and a decreasing width from 11.2 to 1.7 μm. To study 3D migration in a soft (550 Pa) environment, we use self-assembled collagen networks with an average pore size of 3 μm. We then measure the ability of four different cancer cell lines to migrate through these 3D matrices, and correlate the results with cell physical properties including contractility, adhesiveness, cell stiffness, and nuclear volume. Furthermore, we alter cell adhesion by coating the channel walls with different amounts of adhesion proteins, and we increase cell stiffness by overexpression of the nuclear envelope protein lamin A. Although all cell lines are able to migrate through the smallest 1.7 μm channels, we find significant differences in the migration velocity. Cell migration is impeded in cell lines with larger nuclei, lower adhesiveness, and to a lesser degree also in cells with lower contractility and higher stiffness. Our data show that the ability to overcome the steric hindrance of the matrix cannot be attributed to a single cell property but instead arises from a combination of adhesiveness, nuclear volume, contractility, and cell stiffness.