A theory is presented for the steady-state potential of insulated surfaces near exposed high voltages. The term 'insulated surfaces' is used to mean either dielectric surfaces of electrically isolated metallic surfaces. The potential is bounded below by the zero of the material's I-V curve assuming total suppression of secondary electrons, and above by assuming total extraction of secondaries. Within these bounds, the material's surface potential is determined consistently with the solution to Poisson's equation external to the vehicle. The theory is compared with rocket experiments and with SCATHA satellite data. Also, an explanation is suggested for the observed 'snapover' of solar cell coverslips from near plasma ground potential to near the potential of positively biased interconnects with increasing bias voltage.