Despite much work, the connection between dwarf elliptical galaxies (dEs) and dwarf irregulars (dIs) remains unclear. Recently, we found that the surface brightness profiles (SBPs) of dIs in the near-infrared can be well fitted with a hyperbolic secant (sech) function. From sech fits, a tight relationship was derived between the absolute magnitude, central surface brightness, and 21cm line widths, which amounts to a fundamental plane for dIs. Here we examine how closely dEs fit into the dI fundamental plane using published data for 22 dEs in the Virgo cluster and the Local Group. Over a 9 mag interval in absolute magnitude the dEs fall in the plane defined by the dIs. The outstanding overlap suggests more than a casual relationship between the two classes.