A 3-D finite-difference time-domain (FDTD) scheme with controllable stability beyond the stability limit of FDTD is presented. The key to controlling the FDTD stability limit is a spatial filter applied to the electromagnetic field vectors in order to ensure that unstable spatial harmonics are eliminated. A significant advantage of this approach is the simplicity of its incorporation into existing FDTD codes. Moreover, this method is employed as a means to implement a late-time stable 3-D sub-gridding scheme. Applications include waveguide filters and the analysis of screens for near-field sub-wavelength focusing at microwave frequencies.